What alternative term can be used to describe asymmetric cryptographic algorithms?
1. INTRODUCTIONIn the early-1990s, when the commercial Internet was still young (!), security was taken seriously by most users. Many thought that increased security provided comfort to paranoid people while most computer professionals realized that security provided some very basic protections that we all needed? Cryptography for the masses barely existed at that time and was certainly not a topic of common discourse. By the turn of the century, of course, the Internet had grown in size and importance so as to be the provider of essential communication between billions of people around the world and is the ubiquitous tool for commerce, social interaction, and the exchange of an increasing amount of personal information — and we even have a whole form of currency named for cryptography! Show
Security and privacy impacts many applications, ranging from secure commerce and payments to private communications and protecting health care information. One essential aspect for secure communications is that of cryptography. But it is important to note that while cryptography is necessary for secure communications, it is not by itself sufficient. The reader is advised, then, that the topics covered here only describe the first of many steps necessary for better security in any number of situations. This paper has two major purposes. The first is to define some of the terms and concepts behind basic cryptographic methods, and to offer a way to compare the myriad cryptographic schemes in use today. The second is to provide some real examples of cryptography in use today. (See Section A.4 for some additional commentary on this...) DISCLAIMER: Several companies, products, and services are mentioned in this tutorial. Such mention is for example purposes only and, unless explicitly stated otherwise, should not be taken as a recommendation or endorsement by the author. 2. BASIC CONCEPTS OF CRYPTOGRAPHYCryptography — the science of secret writing — is an ancient art; the first documented use of cryptography in writing dates back to circa 1900 B.C. when an Egyptian scribe used non-standard hieroglyphs in an inscription. Some experts argue that cryptography appeared spontaneously sometime after writing was invented, with applications ranging from diplomatic missives to war-time battle plans. It is no surprise, then, that new forms of cryptography came soon after the widespread development of computer communications. In data and telecommunications, cryptography is necessary when communicating over any untrusted medium, which includes just about any network, particularly the Internet. There are five primary functions of cryptography:
In cryptography, we start with the unencrypted data, referred to as plaintext. Plaintext is encrypted into ciphertext, which will in turn (usually) be decrypted back into usable plaintext. The encryption and decryption is based upon the type of cryptography scheme being employed and some form of key. For those who like formulas, this process is sometimes written as: C = Ek(P) where P = plaintext, C = ciphertext, E = the encryption method, D = the decryption method, and k = the key. Given this, there are other functions that might be supported by crypto and other terms that one might hear:
In many of the descriptions below, two communicating parties will be referred to as Alice and Bob; this is the common nomenclature in the crypto field and literature to make it easier to identify the communicating parties. If there is a third and fourth party to the communication, they will be referred to as Carol and Dave, respectively. A malicious party is referred to as Mallory, an eavesdropper as Eve, and a trusted third party as Trent. Finally, cryptography is most closely associated with the development and creation of the mathematical algorithms used to encrypt and decrypt messages, whereas cryptanalysis is the science of analyzing and breaking encryption schemes. Cryptology is the umbrella term referring to the broad study of secret writing, and encompasses both cryptography and cryptanalysis. 3. TYPES OF CRYPTOGRAPHIC ALGORITHMSThere are several ways of classifying cryptographic algorithms. For purposes of this paper, they will be categorized based on the number of keys that are employed for encryption and decryption, and further defined by their application and use. The three types of algorithms that will be discussed are (Figure 1):
FIGURE 1: Three types of cryptography: secret key, public key, and hash function. 3.1. Secret Key CryptographySecret key cryptography methods employ a single key for both encryption and decryption. As shown in Figure 1A, the sender uses the key to encrypt the plaintext and sends the ciphertext to the receiver. The receiver applies the same key to decrypt the message and recover the plaintext. Because a single key is used for both functions, secret key cryptography is also called symmetric encryption. With this form of cryptography, it is obvious that the key must be known to both the sender and the receiver; that, in fact, is the secret. The biggest difficulty with this approach, of course, is the distribution of the key (more on that later in the discussion of public key cryptography). Secret key cryptography schemes are generally categorized as being either stream ciphers or block ciphers.
 A) Self-synchronizing stream cipher. (From Schneier, 1996, Figure 9.8) B) Synchronous stream cipher. (From Schneier, 1996, Figure 9.6) FIGURE 2: Types of stream ciphers. Stream ciphers operate on a single bit (byte or computer word) at a time and implement some form of feedback mechanism so that the key is constantly changing. Stream ciphers come in several flavors but two are worth mentioning here (Figure 2). Self-synchronizing stream ciphers calculate each bit in the keystream as a function of the previous n bits in the keystream. It is termed "self-synchronizing" because the decryption process can stay synchronized with the encryption process merely by knowing how far into the n-bit keystream it is. One problem is error propagation; a garbled bit in transmission will result in n garbled bits at the receiving side. Synchronous stream ciphers generate the keystream in a fashion independent of the message stream but by using the same keystream generation function at sender and receiver. While stream ciphers do not propagate transmission errors, they are, by their nature, periodic so that the keystream will eventually repeat.
FIGURE 3: Feistel cipher. (Source: Wikimedia Commons) A block cipher is so-called because the scheme encrypts one fixed-size block of data at a time. In a block cipher, a given plaintext block will always encrypt to the same ciphertext when using the same key (i.e., it is deterministic) whereas the same plaintext will encrypt to different ciphertext in a stream cipher. The most common construct for block encryption algorithms is the Feistel cipher, named for cryptographer Horst Feistel (IBM). As shown in Figure 3, a Feistel cipher combines elements of substitution, permutation (transposition), and key expansion; these features create a large amount of "confusion and diffusion" (per Claude Shannon) in the cipher. One advantage of the Feistel design is that the encryption and decryption stages are similar, sometimes identical, requiring only a reversal of the key operation, thus dramatically reducing the size of the code or circuitry necessary to implement the cipher in software or hardware, respectively. One of Feistel's early papers describing this operation is "Cryptography and Computer Privacy" (Scientific American, May 1973, 228(5), 15-23). Block ciphers can operate in one of several modes; the following are the most important:
A good overview of these different modes can be found at CRYPTO-IT. Secret key cryptography algorithms in use today — or, at least, important today even if not in use — include:
Although not an SKC scheme, check out Section 5.17 about Shamir's Secret Sharing (SSS). There are several other references that describe interesting algorithms and even SKC codes dating back decades. Two that leap to mind are the Crypto Museum's Crypto List and John J.G. Savard's (albeit old) A Cryptographic Compendium page. 3.2. Public Key CryptographyPublic key cryptography has been said to be the most significant new development in cryptography in the last 300-400 years. Modern PKC was first described publicly by Stanford University professor Martin Hellman and graduate student Whitfield Diffie in 1976. Their paper described a two-key crypto system in which two parties could engage in a secure communication over a non-secure communications channel without having to share a secret key. PKC depends upon the existence of so-called one-way functions, or mathematical functions that are easy to compute whereas their inverse function is relatively difficult to compute. Let me give you two simple examples:
While the examples above are trivial, they do represent two of the functional pairs that are used with PKC; namely, the ease of multiplication and exponentiation versus the relative difficulty of factoring and calculating logarithms, respectively. The mathematical "trick" in PKC is to find a trap door in the one-way function so that the inverse calculation becomes easy given knowledge of some item of information. Generic PKC employs two keys that are mathematically related although knowledge of one key does not allow someone to easily determine the other key. One key is used to encrypt the plaintext and the other key is used to decrypt the ciphertext. The important point here is that it does not matter which key is applied first, but that both keys are required for the process to work (Figure 1B). Because a pair of keys are required, this approach is also called asymmetric cryptography. In PKC, one of the keys is designated the public key and may be advertised as widely as the owner wants. The other key is designated the private key and is never revealed to another party. It is straight-forward to send messages under this scheme. Suppose Alice wants to send Bob a message. Alice encrypts some information using Bob's public key; Bob decrypts the ciphertext using his private key. This method could be also used to prove who sent a message; Alice, for example, could encrypt some plaintext with her private key; when Bob decrypts using Alice's public key, he knows that Alice sent the message (authentication) and Alice cannot deny having sent the message (non-repudiation). Public key cryptography algorithms that are in use today for key exchange or digital signatures include:
For additional information on PKC algorithms, see "Public Key Encryption" (Chapter 8) in Handbook of Applied Cryptography, by A. Menezes, P. van Oorschot, and S. Vanstone (CRC Press, 1996).
3.3. Hash FunctionsHash functions, also called message digests and one-way encryption, are algorithms that, in essence, use no key (Figure 1C). Instead, a fixed-length hash value is computed based upon the plaintext that makes it impossible for either the contents or length of the plaintext to be recovered. Hash algorithms are typically used to provide a digital fingerprint of a file's contents, often used to ensure that the file has not been altered by an intruder or virus. Hash functions are also commonly employed by many operating systems to encrypt passwords. Hash functions, then, provide a mechanism to ensure the integrity of a file. Hash functions are also designed so that small changes in the input produce significant differences in the hash value, for example: Hash string 1: The quick brown fox jumps over the lazy dog Let me reiterate that hashes are one-way encryption. You cannot take a hash and "decrypt" it to find the original string that created it, despite the many web sites that claim or suggest otherwise, such as CrackStation, Hashes.com, MD5 Online, md5thiscracker, OnlineHashCrack, and RainbowCrack. Hash algorithms in common use today include:
Readers might be interested in HashCalc, a Windows-based program that calculates hash values using a dozen algorithms, including MD5, SHA-1 and several variants, RIPEMD-160, and Tiger. Command line utilities that calculate hash values include sha_verify by Dan Mares (Windows; supports MD5, SHA-1, SHA-2) and md5deep (cross-platform; supports MD5, SHA-1, SHA-256, Tiger, and Whirlpool).
Finally, note that certain extensions of hash functions are used for a variety of information security and digital forensics applications, such as:
3.4. Why Three Encryption Techniques?So, why are there so many different types of cryptographic schemes? Why can't we do everything we need with just one? The answer is that each scheme is optimized for some specific cryptographic application(s). Hash functions, for example, are well-suited for ensuring data integrity because any change made to the contents of a message will result in the receiver calculating a different hash value than the one placed in the transmission by the sender. Since it is highly unlikely that two different messages will yield the same hash value, data integrity is ensured to a high degree of confidence. Secret key cryptography, on the other hand, is ideally suited to encrypting messages, thus providing privacy and confidentiality. The sender can generate a session key on a per-message basis to encrypt the message; the receiver, of course, needs the same session key in order to decrypt the message. Key exchange, of course, is a key application of public key cryptography (no pun intended). Asymmetric schemes can also be used for non-repudiation and user authentication; if the receiver can obtain the session key encrypted with the sender's private key, then only this sender could have sent the message. Public key cryptography could, theoretically, also be used to encrypt messages although this is rarely done because secret key cryptography algorithms can generally be executed up to 1000 times faster than public key cryptography algorithms.
FIGURE 4: Use of the three cryptographic techniques for secure communication. Figure 4 puts all of this together and shows how a hybrid cryptographic scheme combines all of these functions to form a secure transmission comprising a digital signature and digital envelope. In this example, the sender of the message is Alice and the receiver is Bob. A digital envelope comprises an encrypted message and an encrypted session key. Alice uses secret key cryptography to encrypt her message using the session key, which she generates at random with each session. Alice then encrypts the session key using Bob's public key. The encrypted message and encrypted session key together form the digital envelope. Upon receipt, Bob recovers the session secret key using his private key and then decrypts the encrypted message. The digital signature is formed in two steps. First, Alice computes the hash value of her message; next, she encrypts the hash value with her private key. Upon receipt of the digital signature, Bob recovers the hash value calculated by Alice by decrypting the digital signature with Alice's public key. Bob can then apply the hash function to Alice's original message, which he has already decrypted (see previous paragraph). If the resultant hash value is not the same as the value supplied by Alice, then Bob knows that the message has been altered; if the hash values are the same, Bob should believe that the message he received is identical to the one that Alice sent. This scheme also provides nonrepudiation since it proves that Alice sent the message; if the hash value recovered by Bob using Alice's public key proves that the message has not been altered, then only Alice could have created the digital signature. Bob also has proof that he is the intended receiver; if he can correctly decrypt the message, then he must have correctly decrypted the session key meaning that his is the correct private key. This diagram purposely suggests a cryptosystem where the session key is used for just a single session. Even if this session key is somehow broken, only this session will be compromised; the session key for the next session is not based upon the key for this session, just as this session's key was not dependent on the key from the previous session. This is known as Perfect Forward Secrecy; you might lose one session key due to a compromise but you won't lose all of them. (This was an issue in the 2014 OpenSSL vulnerability known as Heartbleed.) The system described here is one where we basically encrypt the secret session key with the receiver's public key. While this generic scheme works well, it causes some incompatibilities in practice. RFC 9180, released in early 2022, describes a new approach to building a Hybrid Public Key Encryption (HPKE) process. HPKE was designed specifically to be simple, reusable, and future-proof. A nice description of the process can be found in a blog posting titled, "HPKE: Standardizing Public-Key Encryption (Finally!)" (C. Wood). 3.5. The Significance of Key LengthIn a 1998 article in the industry literature, a writer made the claim that 56-bit keys did not provide as adequate protection for DES at that time as they did in 1975 because computers were 1000 times faster in 1998 than in 1975. Therefore, the writer went on, we needed 56,000-bit keys in 1998 instead of 56-bit keys to provide adequate protection. The conclusion was then drawn that because 56,000-bit keys are infeasible (true), we should accept the fact that we have to live with weak cryptography (false!). The major error here is that the writer did not take into account that the number of possible key values double whenever a single bit is added to the key length; thus, a 57-bit key has twice as many values as a 56-bit key (because 257 is two times 256). In fact, a 66-bit key would have 1024 times more values than a 56-bit key. But this does bring up the question — "What is the significance of key length as it affects the level of protection?" In cryptography, size does matter. The larger the key, the harder it is to crack a block of encrypted data. The reason that large keys offer more protection is almost obvious; computers have made it easier to attack ciphertext by using brute force methods rather than by attacking the mathematics (which are generally well-known anyway). With a brute force attack, the attacker merely generates every possible key and applies it to the ciphertext. Any resulting plaintext that makes sense offers a candidate for a legitimate key. This was the basis, of course, of the EFF's attack on DES. Until the mid-1990s or so, brute force attacks were beyond the capabilities of computers that were within the budget of the attacker community. By that time, however, significant compute power was typically available and accessible. General-purpose computers such as PCs were already being used for brute force attacks. For serious attackers with money to spend, such as some large companies or governments, Field Programmable Gate Array (FPGA) or Application-Specific Integrated Circuits (ASIC) technology offered the ability to build specialized chips that could provide even faster and cheaper solutions than a PC. As an example, the AT&T Optimized Reconfigurable Cell Array (ORCA) FPGA chip cost about $200 and could test 30 million DES keys per second, while a $10 ASIC chip could test 200 million DES keys per second; compare that to a PC which might be able to test 40,000 keys per second. Distributed attacks, harnessing the power of up to tens of thousands of powerful CPUs, are now commonly employed to try to brute-force crypto keys. TABLE 2. Minimum Key Lengths for Symmetric Ciphers.
Table 2 — from a 1996 article discussing both why exporting 40-bit keys was, in essence, no crypto at all and why DES' days were numbered — shows what DES key sizes were needed to protect data from attackers with different time and financial resources. This information was not merely academic; one of the basic tenets of any security system is to have an idea of what you are protecting and from whom are you protecting it! The table clearly shows that a 40-bit key was essentially worthless against even the most unsophisticated attacker. On the other hand, 56-bit keys were fairly strong unless you might be subject to some pretty serious corporate or government espionage. But note that even 56-bit keys were clearly on the decline in their value and that the times in the table were worst cases. So, how big is big enough? DES, invented in 1975, was still in use at the turn of the century, nearly 25 years later. If we take that to be a design criteria (i.e., a 20-plus year lifetime) and we believe Moore's Law ("computing power doubles every 18 months"), then a key size extension of 14 bits (i.e., a factor of more than 16,000) should be adequate. The 1975 DES proposal suggested 56-bit keys; by 1995, a 70-bit key would have been required to offer equal protection and an 85-bit key necessary by 2015. A 256- or 512-bit SKC key will probably suffice for some time because that length keeps us ahead of the brute force capabilities of the attackers. Note that while a large key is good, a huge key may not always be better; for example, expanding PKC keys beyond the current 2048- or 4096-bit lengths doesn't add any necessary protection at this time. Weaknesses in cryptosystems are largely based upon key management rather than weak keys. Much of the discussion above, including the table, is based on the paper "Minimal Key Lengths for Symmetric Ciphers to Provide Adequate Commercial Security" by M. Blaze, W. Diffie, R.L. Rivest, B. Schneier, T. Shimomura, E. Thompson, and M. Wiener (1996). The most effective large-number factoring methods today use a mathematical Number Field Sieve to find a certain number of relationships and then uses a matrix operation to solve a linear equation to produce the two prime factors. The sieve step actually involves a large number of operations that can be performed in parallel; solving the linear equation, however, requires a supercomputer. Indeed, finding the solution to the RSA-140 challenge in February 1999 — factoring a 140-digit (465-bit) prime number — required 200 computers across the Internet about 4 weeks for the first step and a Cray computer 100 hours and 810 MB of memory to do the second step. In early 1999, Shamir (of RSA fame) described a new machine that could increase factorization speed by 2-3 orders of magnitude. Although no detailed plans were provided nor is one known to have been built, the concepts of TWINKLE (The Weizmann Institute Key Locating Engine) could result in a specialized piece of hardware that would cost about $5000 and have the processing power of 100-1000 PCs. There still appear to be many engineering details that have to be worked out before such a machine could be built. Furthermore, the hardware improves the sieve step only; the matrix operation is not optimized at all by this design and the complexity of this step grows rapidly with key length, both in terms of processing time and memory requirements. Nevertheless, this plan conceptually puts 512-bit keys within reach of being factored. Although most PKC schemes allow keys that are 1024 bits and longer, Shamir claims that 512-bit RSA keys "protect 95% of today's E-commerce on the Internet." (See Bruce Schneier's Crypto-Gram (May 15, 1999) for more information.) It is also interesting to note that while cryptography is good and strong cryptography is better, long keys may disrupt the nature of the randomness of data files. Shamir and van Someren ("Playing hide and seek with stored keys") have noted that a new generation of viruses can be written that will find files encrypted with long keys, making them easier to find by intruders and, therefore, more prone to attack. Finally, U.S. government policy has tightly controlled the export of crypto products since World War II. Until the mid-1990s, export outside of North America of cryptographic products using keys greater than 40 bits in length was prohibited, which made those products essentially worthless in the marketplace, particularly for electronic commerce; today, crypto products are widely available on the Internet without restriction. The U.S. Department of Commerce Bureau of Industry and Security maintains an Encryption FAQ web page with more information about the current state of encryption registration.
On a related topic, public key crypto schemes can be used for several purposes, including key exchange, digital signatures, authentication, and more. In those PKC systems used for SKC key exchange, the PKC key lengths are chosen so as to be resistant to some selected level of attack. The length of the secret keys exchanged via that system have to have at least the same level of attack resistance. Thus, the three parameters of such a system — system strength, secret key strength, and public key strength — must be matched. This topic is explored in more detail in Determining Strengths For Public Keys Used For Exchanging Symmetric Keys (RFC 3766). 4. TRUST MODELSSecure use of cryptography requires trust. While secret key cryptography can ensure message confidentiality and hash codes can ensure integrity, none of this works without trust. In SKC, Alice and Bob had to share a secret key. PKC solved the secret distribution problem, but how does Alice really know that Bob is who he says he is? Just because Bob has a public and private key, and purports to be "Bob," how does Alice know that a malicious person (Mallory) is not pretending to be Bob? There are a number of trust models employed by various cryptographic schemes. This section will explore three of them:
Each of these trust models differs in complexity, general applicability, scope, and scalability. 4.1. PGP Web of TrustPretty Good Privacy (described more below in Section 5.5) is a widely used private e-mail scheme based on public key methods. A PGP user maintains a local keyring of all their known and trusted public keys. The user makes their own determination about the trustworthiness of a key using what is called a "web of trust."
FIGURE 5: GPG keychain. Figure 5 shows a PGP-formatted keychain from the GNU Privacy Guard (GPG) software, an implementation of the OpenPGP standard. This is a section of my keychain, so only includes public keys from individuals whom I know and, presumably, trust. Note that keys are associated with e-mail addresses rather than individual names. In general, the PGP Web of trust works as follows. Suppose that Alice needs Bob's public key. Alice could just ask Bob for it directly via e-mail or download the public key from a PGP key server; this server might a well-known PGP key repository or a site that Bob maintains himself. In fact, Bob's public key might be stored or listed in many places. (My public key, for example, can be found at https://www.garykessler.net/pubkey.html or at several public PGP key servers, including https://keys.openpgp.org.) Alice is prepared to believe that Bob's public key, as stored at these locations, is valid. Suppose Carol claims to hold Bob's public key and offers to give the key to Alice. How does Alice know that Carol's version of Bob's key is valid or if Carol is actually giving Alice a key that will allow Mallory access to messages? The answer is, "It depends." If Alice trusts Carol and Carol says that she thinks that her version of Bob's key is valid, then Alice may — at her option — trust that key. And trust is not necessarily transitive; if Dave has a copy of Bob's key and Carol trusts Dave, it does not necessarily follow that Alice trusts Dave even if she does trust Carol. The point here is that who Alice trusts and how she makes that determination is strictly up to Alice. PGP makes no statement and has no protocol about how one user determines whether they trust another user or not. In any case, encryption and signatures based on public keys can only be used when the appropriate public key is on the user's keyring. 4.2. KerberosKerberos is a commonly used authentication scheme on the Internet. Developed by MIT's Project Athena, Kerberos is named for the three-headed dog who, according to Greek mythology, guards the entrance of Hades (rather than the exit, for some reason!). Kerberos employs a client/server architecture and provides user-to-server authentication rather than host-to-host authentication. In this model, security and authentication will be based on secret key technology where every host on the network has its own secret key. It would clearly be unmanageable if every host had to know the keys of all other hosts so a secure, trusted host somewhere on the network, known as a Key Distribution Center (KDC), knows the keys for all of the hosts (or at least some of the hosts within a portion of the network, called a realm). In this way, when a new node is brought online, only the KDC and the new node need to be configured with the node's key; keys can be distributed physically or by some other secure means.
FIGURE 6: Kerberos architecture. The Kerberos Server/KDC has two main functions (Figure 6), known as the Authentication Server (AS) and Ticket-Granting Server (TGS). The steps in establishing an authenticated session between an application client and the application server are:
The current version of this protocol is Kerberos V5 (described in RFC 1510). While the details of their operation, functional capabilities, and message formats are different, the conceptual overview above pretty much holds for both. One primary difference is that Kerberos V4 uses only DES to generate keys and encrypt messages, while V5 allows other schemes to be employed (although DES is still the most widely algorithm used). 4.3. Public Key Certificates and Certificate AuthoritiesCertificates and Certificate Authorities (CA) are necessary for widespread use of cryptography for e-commerce applications. While a combination of secret and public key cryptography can solve the business issues discussed above, crypto cannot alone address the trust issues that must exist between a customer and vendor in the very fluid, very dynamic e-commerce relationship. How, for example, does one site obtain another party's public key? How does a recipient determine if a public key really belongs to the sender? How does the recipient know that the sender is using their public key for a legitimate purpose for which they are authorized? When does a public key expire? How can a key be revoked in case of compromise or loss? The basic concept of a certificate is one that is familiar to all of us. A driver's license, credit card, or SCUBA certification, for example, identify us to others, indicate something that we are authorized to do, have an expiration date, and identify the authority that granted the certificate. As complicated as this may sound, it really isn't. Consider driver's licenses. I have one issued by the State of Florida. The license establishes my identity, indicates the type of vehicles that I can operate and the fact that I must wear corrective lenses while doing so, identifies the issuing authority, and notes that I am an organ donor. When I drive in other states, the other jurisdictions throughout the U.S. recognize the authority of Florida to issue this "certificate" and they trust the information it contains. When I leave the U.S., everything changes. When I am in Aruba, Australia, Canada, Israel, and many other countries, they will accept not the Florida license, per se, but any license issued in the U.S. This analogy represents the certificate trust chain, where even certificates carry certificates. For purposes of electronic transactions, certificates are digital documents. The specific functions of the certificate include:
Typically, a certificate contains a public key, a name, an expiration date, the name of the authority that issued the certificate (and, therefore, is vouching for the identity of the user), a serial number, any pertinent policies describing how the certificate was issued and/or how the certificate may be used, the digital signature of the certificate issuer, and perhaps other information.
FIGURE 7: VeriSign Class 3 certificate. A sample abbreviated certificate is shown in Figure 7. This is a typical certificate found in a browser, in this case, Mozilla Firefox (MacOS). While this is a certificate issued by VeriSign, many root-level certificates can be found shipped with browsers. When the browser makes a connection to a secure Web site, the Web server sends its public key certificate to the browser. The browser then checks the certificate's signature against the public key that it has stored; if there is a match, the certificate is taken as valid and the Web site verified by this certificate is considered to be "trusted." The most widely accepted certificate format is the one defined in International Telecommunication Union Telecommunication Standardization Sector (ITU-T) Recommendation X.509. Rec. X.509 is a specification used around the world and any applications complying with X.509 can share certificates. Most certificates today comply with X.509 Version 3 and contain the following information:
Certificate authorities are the repositories for public keys and can be any agency that issues certificates. A company, for example, may issue certificates to its employees, a college/university to its students, a store to its customers, an Internet service provider to its users, or a government to its constituents. When a sender needs an intended receiver's public key, the sender must get that key from the receiver's CA. That scheme is straight-forward if the sender and receiver have certificates issued by the same CA. If not, how does the sender know to trust the foreign CA? One industry wag has noted, about trust: "You are either born with it or have it granted upon you." Thus, some CAs will be trusted because they are known to be reputable, such as the CAs operated by AT&T Services, Comodo, DigiCert (formerly GTE Cybertrust), EnTrust, Broadcom (formerly Symantec, formerly VeriSign), and Thawte. CAs, in turn, form trust relationships with other CAs. Thus, if a user queries a foreign CA for information, the user may ask to see a list of CAs that establish a "chain of trust" back to the user. One major feature to look for in a CA is their identification policies and procedures. When a user generates a key pair and forwards the public key to a CA, the CA has to check the sender's identification and takes any steps necessary to assure itself that the request is really coming from the advertised sender. Different CAs have different identification policies and will, therefore, be trusted differently by other CAs. Verification of identity is just one of many issues that are part of a CA's Certification Practice Statement (CPS) and policies; other issues include how the CA protects the public keys in its care, how lost or compromised keys are revoked, and how the CA protects its own private keys. As a final note, CAs are not immune to attack and certificates themselves are able to be counterfeited. One of the first such episodes occurred at the turn of the century; on January 29 and 30, 2001, two VeriSign Class 3 code-signing digital certificates were issued to an individual who fraudulently claimed to be a Microsoft employee (CERT/CC CA-2001-04 and Microsoft Security Bulletin MS01-017 - Critical). Problems have continued over the years; good write-ups on this can be found at "Another Certification Authority Breached (the 12th!)" and "How Cybercrime Exploits Digital Certificates." Readers are also urged to read "Certification Authorities Under Attack: A Plea for Certificate Legitimation" (Oppliger, R., January/February 2014, IEEE Internet Computing, 18(1), 40-47). As a partial way to address this issue, the Internet Security Research Group (ISRG) designed the Automated Certificate Management Environment (ACME) protocol. ACME is a communications protocol that streamlines the process of deploying a Public Key Infrastructure (PKI) by automating interactions between CAs and Web servers that wish to obtain a certificate. More information can be found at the Let's Encrypt Web site, an ACME-based CA service provided by the ISRG. 4.4. SummaryThe paragraphs above describe three very different trust models. It is hard to say that any one is better than the others; it depends upon your application. One of the biggest and fastest growing applications of cryptography today, though, is electronic commerce (e-commerce), a term that itself begs for a formal definition. PGP's web of trust is easy to maintain and very much based on the reality of users as people. The model, however, is limited; just how many public keys can a single user reliably store and maintain? And what if you are using the "wrong" computer when you want to send a message and can't access your keyring? How easy it is to revoke a key if it is compromised? PGP may also not scale well to an e-commerce scenario of secure communication between total strangers on short-notice. Kerberos overcomes many of the problems of PGP's web of trust, in that it is scalable and its scope can be very large. However, it also requires that the Kerberos server have a priori knowledge of all client systems prior to any transactions, which makes it unfeasible for "hit-and-run" client/server relationships as seen in e-commerce. Certificates and the collection of CAs will form a PKI. In the early days of the Internet, every host had to maintain a list of every other host; the Domain Name System (DNS) introduced the idea of a distributed database for this purpose and the DNS is one of the key reasons that the Internet has grown as it has. A PKI will fill a similar void in the e-commerce and PKC realm. While certificates and the benefits of a PKI are most often associated with electronic commerce, the applications for PKI are much broader and include secure electronic mail, payments and electronic checks, Electronic Data Interchange (EDI), secure transfer of Domain Name System (DNS) and routing information, electronic forms, and digitally signed documents. A single "global PKI" is still many years away, that is the ultimate goal of today's work as international electronic commerce changes the way in which we do business in a similar way in which the Internet has changed the way in which we communicate. 5. CRYPTOGRAPHIC ALGORITHMS IN ACTIONThe paragraphs above have provided an overview of the different types of cryptographic algorithms, as well as some examples of some available protocols and schemes. Table 3 provides a list of some other noteworthy schemes and cryptosystems employed — or proposed — for a variety of functions, most notably electronic commerce and secure communication. The paragraphs below will show several real cryptographic applications that many of us employ (knowingly or not) everyday for password protection and private communication. Some of the schemes described below never were widely deployed but are still historically interesting, thus remain included here. This list is, by no means, exhaustive but describes items that are of significant current and/or historic importance (a subjective judgement, to be sure). TABLE 3. Other Crypto Algorithms and Systems of Note.
5.1. Password ProtectionNearly all modern multiuser computer and network operating systems employ passwords at the very least to protect and authenticate users accessing computer and/or network resources. But passwords are not typically kept on a host or server in plaintext, but are generally encrypted using some sort of hash scheme. A) /etc/passwd file root:Jbw6BwE4XoUHo:0:0:root:/root:/bin/bash carol:FM5ikbQt1K052:502:100:Carol Monaghan:/home/carol:/bin/bash alex:LqAi7Mdyg/HcQ:503:100:Alex Insley:/home/alex:/bin/bash gary:FkJXupRyFqY4s:501:100:Gary Kessler:/home/gary:/bin/bash todd:edGqQUAaGv7g6:506:101:Todd Pritsky:/home/todd:/bin/bash josh:FiH0ONcjPut1g:505:101:Joshua Kessler:/home/webroot:/bin/bash B.1) /etc/passwd file (with shadow passwords) root:x:0:0:root:/root:/bin/bash carol:x:502:100:Carol Monaghan:/home/carol:/bin/bash alex:x:503:100:Alex Insley:/home/alex:/bin/bash gary:x:501:100:Gary Kessler:/home/gary:/bin/bash todd:x:506:101:Todd Pritsky:/home/todd:/bin/bash josh:x:505:101:Joshua Kessler:/home/webroot:/bin/bash B.2) /etc/shadow file root:AGFw$1$P4u/uhLK$l2.HP35rlu65WlfCzq:11449:0:99999:7::: carol:kjHaN%35a8xMM8a/0kMl1?fwtLAM.K&kw.:11449:0:99999:7::: alex:1$1KKmfTy0a7#3.LL9a8H71lkwn/.hH22a:11449:0:99999:7::: gary:9ajlknknKJHjhnu7298ypnAIJKL$Jh.hnk:11449:0:99999:7::: todd:798POJ90uab6.k$klPqMt%alMlprWqu6$.:11492:0:99999:7::: josh:Awmqpsui*787pjnsnJJK%aappaMpQo07.8:11492:0:99999:7::: FIGURE 8: Sample entries in Unix/Linux password files. Unix/Linux, for example, uses a well-known hash via its crypt() function. Passwords are stored in the /etc/passwd file (Figure 8A); each record in the file contains the username, hashed password, user's individual and group numbers, user's name, home directory, and shell program; these fields are separated by colons (:). Note that each password is stored as a 13-byte string. The first two characters are actually a salt, randomness added to each password so that if two users have the same password, they will still be encrypted differently; the salt, in fact, provides a means so that a single password might have 4096 different encryptions. The remaining 11 bytes are the password hash, calculated using DES. As it happens, the /etc/passwd file is world-readable on Unix systems. This fact, coupled with the weak encryption of the passwords, resulted in the development of the shadow password system where passwords are kept in a separate, non-world-readable file used in conjunction with the normal password file. When shadow passwords are used, the password entry in /etc/passwd is replaced with a "*" or "x" (Figure 8B.1) and the MD5 hash of the passwords are stored in /etc/shadow along with some other account information (Figure 8B.2). Windows NT uses a similar scheme to store passwords in the Security Access Manager (SAM) file. In the NT case, all passwords are hashed using the MD4 algorithm, resulting in a 128-bit (16-byte) hash value (they are then obscured using an undocumented mathematical transformation that was a secret until distributed on the Internet). The password password, for example, might be stored as the hash value (in hexadecimal) 60771b22d73c34bd4a290a79c8b09f18. Passwords are not saved in plaintext on computer systems precisely so they cannot be easily compromised. For similar reasons, we don't want passwords sent in plaintext across a network. But for remote logon applications, how does a client system identify itself or a user to the server? One mechanism, of course, is to send the password as a hash value and that, indeed, may be done. A weakness of that approach, however, is that an intruder can grab the password off of the network and use an off-line attack (such as a dictionary attack where an attacker takes every known word and encrypts it with the network's encryption algorithm, hoping eventually to find a match with a purloined password hash). In some situations, an attacker only has to copy the hashed password value and use it later on to gain unauthorized entry without ever learning the actual password. An even stronger authentication method uses the password to modify a shared secret between the client and server, but never allows the password in any form to go across the network. This is the basis for the Challenge Handshake Authentication Protocol (CHAP), the remote logon process used by Windows NT. As suggested above, Windows NT passwords are stored in a security file on a server as a 16-byte hash value. In truth, Windows NT stores two hashes; a weak hash based upon the old LAN Manager (LanMan) scheme and the newer NT hash. When a user logs on to a server from a remote workstation, the user is identified by the username, sent across the network in plaintext (no worries here; it's not a secret anyway!). The server then generates a 64-bit random number and sends it to the client (also in plaintext). This number is the challenge. Using the LanMan scheme, the client system then encrypts the challenge using DES. Recall that DES employs a 56-bit key, acts on a 64-bit block of data, and produces a 64-bit output. In this case, the 64-bit data block is the random number. The client actually uses three different DES keys to encrypt the random number, producing three different 64-bit outputs. The first key is the first seven bytes (56 bits) of the password's hash value, the second key is the next seven bytes in the password's hash, and the third key is the remaining two bytes of the password's hash concatenated with five zero-filled bytes. (So, for the example above, the three DES keys would be 60771b22d73c34, bd4a290a79c8b0, and 9f180000000000.) Each key is applied to the random number resulting in three 64-bit outputs, which comprise the response. Thus, the server's 8-byte challenge yields a 24-byte response from the client and this is all that would be seen on the network. The server, for its part, does the same calculation to ensure that the values match. There is, however, a significant weakness to this system. Specifically, the response is generated in such a way as to effectively reduce 16-byte hash to three smaller hashes, of length seven, seven, and two, respectively. Thus, a password cracker has to break at most a 7-byte hash. One Windows NT vulnerability test program that I used in the past reported passwords that were "too short," defined as "less than 8 characters." When I asked how the program knew that passwords were too short, the software's salespeople suggested to me that the program broke the passwords to determine their length. This was, in fact, not the case at all; all the software really had to do was to look at the last eight bytes of the Windows NT LanMan hash to see that the password was seven or fewer characters. Consider the following example, showing the LanMan hash of two different short passwords (take a close look at the last 8 bytes):
Note that the NT hash provides no such clue:
It is worth noting that the discussion above describes the Microsoft version of CHAP, or MS-CHAP (MS-CHAPv2 is described in RFC 2759). MS-CHAP assumes that it is working with hashed values of the password as the key to encrypting the challenge. More traditional CHAP (RFC 1994) assumes that it is starting with passwords in plaintext. The relevance of this observation is that a CHAP client, for example, cannot be authenticated by an MS-CHAP server; both client and server must use the same CHAP version. 5.2. Diffie-Hellman Key ExchangeDiffie and Hellman introduced the concept of public key cryptography. The mathematical "trick" of Diffie-Hellman key exchange is that it is relatively easy to compute exponents compared to computing discrete logarithms. Diffie-Hellman allows two parties — the ubiquitous Alice and Bob — to generate a secret key; they need to exchange some information over an unsecure communications channel to perform the calculation but an eavesdropper cannot determine the shared secret key based upon this information. Diffie-Hellman works like this. Alice and Bob start by agreeing on a large prime number, N. They also have to choose some number G so that G There is actually another constraint on G, namely that it must be primitive with respect to N.
Primitive is a definition that is a little beyond the scope of our discussion but basically G is primitive to N if the set of N-1 values of Gi mod N for i = (1,N-1) are all different. As an example, 2 is not primitive to 7 because the set of powers of 2 from 1 to 6, mod 7 (i.e., 21 mod 7, 22 mod 7, ..., 26 mod 7) = {2,4,1,2,4,1}. On the other hand, 3 is primitive to 7 because the set of powers of 3 from 1 to 6, mod 7 = {3,2,6,4,5,1}. (The
definition of primitive introduced a new term to some readers, namely mod. The phrase x mod y (and read as written!) means "take the remainder after dividing x by y." Thus, 1 mod 7 = 1, 9 mod 6 = 3, and 8 mod 8 = 0. Read more about the modulo function in the appendix.) Anyway, either Alice or Bob selects N and G; they then tell the other party what the values are. Alice and Bob then
work independently (Figure 9): FIGURE 9: Diffie-Hellman key exchange model. Note that XA and XB are kept secret while YA and YB are openly shared; these are the private and public keys, respectively. Based on their own private key and the public key learned from the other party, Alice and Bob have computed their secret keys, KA and KB, respectively, which are equal to
GXAXB mod N. Perhaps a small example will help here. Although Alice and Bob will really choose large values for N and G, I will use small values for example only; let's use N=7 and G=3, as shown in Figure 10. FIGURE 10: Diffie-Hellman key exchange example. In this example, then, Alice and Bob will both find the secret key 1 which is, indeed, 36 mod 7 (i.e.,
GXAXB = 32x3). If an eavesdropper (Eve) was listening in on the information exchange between Alice and Bob, she would learn G, N, YA, and YB which is a lot of information but insufficient to compromise the key; as long as XA and XB remain unknown, K is safe. As stated above, calculating Y = GX is a lot easier than finding X = logG Y.
A short digression on modulo arithmetic. In the paragraph above, we noted that 36 mod 7 = 1. This can be confirmed, of course, by noting that: 36 = 729 = 104*7 + 1 There is a nice property of modulo arithmetic, however, that makes this determination a little easier, namely: (a mod x)(b mod x) = (ab mod x). Therefore, one possible shortcut is to note that 36 = (33)(33). Therefore, 36 mod
7 = (33 mod 7)(33 mod 7) = (27 mod 7)(27 mod 7) = 6*6 mod 7 = 36 mod 7 = 1. Diffie-Hellman can also be used to allow key sharing amongst multiple users. Note again that the Diffie-Hellman algorithm is used to generate secret keys, not to encrypt and decrypt messages. Unlike Diffie-Hellman, RSA can be used for key exchange as well as digital signatures and the encryption of small blocks of
data. Today, RSA is primarily used to encrypt the session key used for secret key encryption (message integrity) or the message's hash value (digital signature). RSA's mathematical hardness comes from the ease in calculating large numbers and the difficulty in finding the prime factors of those large numbers. Although employed with numbers using hundreds of digits, the math behind RSA is relatively straight-forward. To create an RSA public/private key pair, here are the basic steps: The public key is the number pair (n,e). Although these values are publicly known, it is computationally
infeasible to determine d from n and e if p and q are large enough. To encrypt a message, M, with the public key, create the ciphertext, C, using the equation: The receiver then decrypts the ciphertext with the private key using the equation: Now, this might look a bit complex and, indeed, the mathematics does take a lot of computer power given the large size of the numbers; since p and q may be 100 digits
(decimal) or more, d and e will be about the same size and n may be over 200 digits. Nevertheless, a simple example may help. In this example, the values for p, q, e, and d are purposely chosen to be very small and the reader will see exactly how badly these values perform, but hopefully the algorithm will be adequately demonstrated: I choose this trivial example because the value of n is so small (in particular, the value M cannot exceed n). But here is a more realistic example using larger d, e, and n values, as well as a more meaningful message; thanks to Barry Steyn for
permission to use values from his How RSA Works With Examples page. Let's say that we have chosen p and q so that we have the following value for n: 14590676800758332323018693934907063529240187237535716439958187 Let's also suppose that we have selected the public key, e, and private key, d, as follows: 65537 89489425009274444368228545921773093919669586065884257445497854 Now suppose that our message (M) is the character string "attack at dawn" which has the numeric value (after converting the ASCII characters to a bit string and interpreting that bit string as a decimal number) of
1976620216402300889624482718775150. The encryption phase uses the formula C = Me mod n, so C has the value: 35052111338673026690212423937053328511880760811579981620642802 The decryption phase uses the formula M = Cd mod n, so M has the value that matches our original plaintext: 1976620216402300889624482718775150 This more realistic example gives just a clue as to how large the numbers are that are used in the real world implementations. RSA keylengths of 512 and 768 bits are
considered to be pretty weak. The minimum suggested RSA key is 1024 bits; 2048 and 3072 bits are even better. As an aside, Adam Back (http://www.cypherspace.org/~adam/) wrote a two-line Perl script to implement RSA. It employs dc, an arbitrary precision arithmetic package that ships with most UNIX systems: 5.4. DES, Breaking DES, and DES VariantsThe Data Encryption Standard (DES) started life in the mid-1970s, adopted by the National Bureau of Standards (NBS) [now the National Institute of Standards and Technology (NIST)] as Federal Information Processing Standard 46 (FIPS PUB 46-3) and by the American National Standards Institute (ANSI) as X3.92. As mentioned earlier, DES uses the Data Encryption Algorithm (DEA), a secret key block-cipher employing a 56-bit key operating on 64-bit blocks. FIPS PUB 81 describes four modes of DES operation: Electronic Codebook (ECB), Cipher Block Chaining (CBC), Cipher Feedback (CFB), and Output Feedback (OFB). Despite all of these options, ECB is the most commonly deployed mode of operation. NIST finally declared DES obsolete in 2004, and withdrew FIPS PUB 46-3, 74, and 81 (Federal Register, July 26, 2004, 69(142), 44509-44510). Although other block ciphers have replaced DES, it is still interesting to see how DES encryption is performed; not only is it sort of neat, but DES was the first crypto scheme commonly seen in non-governmental applications and was the catalyst for modern "public" cryptography and the first public Feistel cipher. DES still remains in many products — and cryptography students and cryptographers will continue to study DES for years to come. DES Operational Overview DES uses a 56-bit key. In fact, the 56-bit key is divided into eight 7-bit blocks and an 8th odd parity bit is added to each block (i.e., a "0" or "1" is added to the block so that there are an odd number of 1 bits in each 8-bit block). By using the 8 parity bits for rudimentary error detection, a DES key is actually 64 bits in length for computational purposes although it only has 56 bits worth of randomness, or entropy (See Section A.3 for a brief discussion of entropy and information theory).
FIGURE 11: DES enciphering algorithm. DES then acts on 64-bit blocks of the plaintext, invoking 16 rounds of permutations, swaps, and substitutes, as shown in Figure 11. The standard includes tables describing all of the selection, permutation, and expansion operations mentioned below; these aspects of the algorithm are not secrets. The basic DES steps are:
Consider this example using DES in CBC mode with the following 56-bit key and input:
Input character string (ASCII/IA5): +2903015-08091765 Output string (hex): 0x9812CB620B2E9FD3AD90DE2B92C6BBB6C52753AC43E1AFA6 Observe that we start with a 17-byte input message. DES acts on eight bytes at a time, so this message is padded to 24 bytes and provides three "inputs" to the cipher algorithm (we don't see the padding here; it is appended by the DES code). Since we have three input blocks, we get 24 bytes of output from the three 64-bit (eight byte) output blocks. If you want to test this, a really good free, online DES calculator hosted by the Information Security Group at University College London. An excellent step-by-step example of DES can also be found at J. Orlin Grabbe's The DES Algorithm Illustrated page. NOTE: You'll notice that the output above is shown in BASE64. BASE64 is a 64-character alphabet — i.e., a six-bit character code composed of upper- and lower-case letters, the digits 0-9, and a few punctuation characters — that is commonly used as a way to display binary data. A byte has eight bits, or 256 values, but not all 256 ASCII characters are defined and/or printable. BASE64, simply, takes a binary string (or file), divides it into six-bit blocks, and translates each block into a printable character. More information about BASE64 can be found at my BASE64 Alphabet page or at Wikipedia. Breaking DES The mainstream cryptographic community has long held that DES's 56-bit key was too short to withstand a brute-force attack from modern computers. Remember Moore's Law: computer power doubles every 18 months. Given that increase in power, a key that could withstand a brute-force guessing attack in 1975 could hardly be expected to withstand the same attack a quarter century later. DES is even more vulnerable to a brute-force attack because it is often used to encrypt words, meaning that the entropy of the 64-bit block is, effectively, greatly reduced. That is, if we are encrypting random bit streams, then a given byte might contain any one of 28 (256) possible values and the entire 64-bit block has 264, or about 18.5 quintillion, possible values. If we are encrypting words, however, we are most likely to find a limited set of bit patterns; perhaps 70 or so if we account for upper and lower case letters, the numbers, space, and some punctuation. This means that only about ¼ of the bit combinations of a given byte are likely to occur. Despite this criticism, the U.S. government insisted throughout the mid-1990s that 56-bit DES was secure and virtually unbreakable if appropriate precautions were taken. In response, RSA Laboratories sponsored a series of cryptographic challenges to prove that DES was no longer appropriate for use. DES Challenge I was launched in March 1997. It was completed in 84 days by R. Verser in a collaborative effort using thousands of computers on the Internet. The first DES Challenge II lasted 40 days in early 1998. This problem was solved by distributed.net, a worldwide distributed computing network using the spare CPU cycles of computers around the Internet (participants in distributed.net's activities load a client program that runs in the background, conceptually similar to the SETI @Home "Search for Extraterrestrial Intelligence" project). The distributed.net systems were checking 28 billion keys per second by the end of the project. The second DES Challenge II lasted less than 3 days. On July 17, 1998, the Electronic Frontier Foundation (EFF) announced the construction of hardware that could brute-force a DES key in an average of 4.5 days. Called Deep Crack, the device could check 90 billion keys per second and cost only about $220,000 including design (it was erroneously and widely reported that subsequent devices could be built for as little as $50,000). Since the design is scalable, this suggests that an organization could build a DES cracker that could break 56-bit keys in an average of a day for as little as $1,000,000. Information about the hardware design and all software can be obtained from the EFF. The DES Challenge III, launched in January 1999, was broken is less than a day by the combined efforts of Deep Crack and distributed.net. This is widely considered to have been the final nail in DES's coffin. The Deep Crack algorithm is actually quite interesting. The general approach that the DES Cracker Project took was not to break the algorithm mathematically but instead to launch a brute-force attack by guessing every possible key. A 56-bit key yields 256, or about 72 quadrillion, possible values. So the DES cracker team looked for any shortcuts they could find! First, they assumed that some recognizable plaintext would appear in the decrypted string even though they didn't have a specific known plaintext block. They then applied all 256 possible key values to the 64-bit block (I don't mean to make this sound simple!). The system checked to see if the decrypted value of the block was "interesting," which they defined as bytes containing one of the alphanumeric characters, space, or some punctuation. Since the likelihood of a single byte being "interesting" is about ¼, then the likelihood of the entire 8-byte stream being "interesting" is about ¼8, or 1/65536 (½16). This dropped the number of possible keys that might yield positive results to about 240, or about a trillion. They then made the assumption that an "interesting" 8-byte block would be followed by another "interesting" block. So, if the first block of ciphertext decrypted to something interesting, they decrypted the next block; otherwise, they abandoned this key. Only if the second block was also "interesting" did they examine the key closer. Looking for 16 consecutive bytes that were "interesting" meant that only 224, or 16 million, keys needed to be examined further. This further examination was primarily to see if the text made any sense. Note that possible "interesting" blocks might be 1hJ5&aB7 or DEPOSITS; the latter is more likely to produce a better result. And even a slow laptop today can search through lists of only a few million items in a relatively short period of time. (Interested readers are urged to read Cracking DES and EFF's Cracking DES page.) It is well beyond the scope of this paper to discuss other forms of breaking DES and other codes. Nevertheless, it is worth mentioning a couple of forms of cryptanalysis that have been shown to be effective against DES. Differential cryptanalysis, invented in 1990 by E. Biham and A. Shamir (of RSA fame), is a chosen-plaintext attack. By selecting pairs of plaintext with particular differences, the cryptanalyst examines the differences in the resultant ciphertext pairs. Linear plaintext, invented by M. Matsui, uses a linear approximation to analyze the actions of a block cipher (including DES). Both of these attacks can be more efficient than brute force. DES Variants Once DES was "officially" broken, several variants appeared. But none of them came overnight; work at hardening DES had already been underway. In the early 1990s, there was a proposal to increase the security of DES by effectively increasing the key length by using multiple keys with multiple passes. But for this scheme to work, it had to first be shown that the DES function is not a group, as defined in mathematics. If DES was a group, then we could show that for two DES keys, X1 and X2, applied to some plaintext (P), we can find a single equivalent key, X3, that would provide the same result; i.e., EX2(EX1(P)) = EX3(P) where EX(P) represents DES encryption of some plaintext P using DES key X. If DES were a group, it wouldn't matter how many keys and passes we applied to some plaintext; we could always find a single 56-bit key that would provide the same result. As it happens, DES was proven to not be a group so that as we apply additional keys and passes, the effective key length increases. One obvious choice, then, might be to use two keys and two passes, yielding an effective key length of 112 bits. Let's call this Double-DES. The two keys, Y1 and Y2, might be applied as follows: C = EY2(EY1(P)) where EY(P) and DY(C) represent DES encryption and decryption, respectively, of some plaintext P and ciphertext C, respectively, using DES key Y. So far, so good. But there's an interesting attack that can be launched against this "Double-DES" scheme. First, notice that the applications of the formula above can be thought of with the following individual steps (where C' and P' are intermediate results): C' = EY1(P) and C = EY2(C') Unfortunately, C'=P'. That leaves us vulnerable to a simple known plaintext attack (sometimes called "Meet-in-the-middle") where the attacker knows some plaintext (P) and its matching ciphertext (C). To obtain C', the attacker needs to try all 256 possible values of Y1 applied to P; to obtain P', the attacker needs to try all 256 possible values of Y2 applied to C. Since C'=P', the attacker knows when a match has been achieved — after only 256 + 256 = 257 key searches, only twice the work of brute-forcing DES. So "Double-DES" is not a good solution. Triple-DES (3DES), based upon the Triple Data Encryption Algorithm (TDEA), is described in FIPS PUB 46-3. 3DES, which is not susceptible to a meet-in-the-middle attack, employs three DES passes and one, two, or three keys called K1, K2, and K3. Generation of the ciphertext (C) from a block of plaintext (P) is accomplished by: C = EK3(DK2(EK1(P))) where EK(P) and DK(P) represent DES encryption and decryption, respectively, of some plaintext P using DES key K. (For obvious reasons, this is sometimes referred to as an encrypt-decrypt-encrypt mode operation.) Decryption of the ciphertext into plaintext is accomplished by: P = DK1(EK2(DK3(C))) The use of three, independent 56-bit keys provides 3DES with an effective key length of 168 bits. The specification also defines use of two keys where, in the operations above, K3 = K1; this provides an effective key length of 112 bits. Finally, a third keying option is to use a single key, so that K3 = K2 = K1 (in this case, the effective key length is 56 bits and 3DES applied to some plaintext, P, will yield the same ciphertext, C, as normal DES would with that same key). Given the relatively low cost of key storage and the modest increase in processing due to the use of longer keys, the best recommended practices are that 3DES be employed with three keys. Another variant of DES, called DESX, is due to Ron Rivest. Developed in 1996, DESX is a very simple algorithm that greatly increases DES's resistance to brute-force attacks without increasing its computational complexity. In DESX, the plaintext input is XORed with 64 additional key bits prior to encryption and the output is likewise XORed with the 64 key bits. By adding just two XOR operations, DESX has an effective keylength of 120 bits against an exhaustive key-search attack. As it happens, DESX is no more immune to other types of more sophisticated attacks, such as differential or linear cryptanalysis, but brute-force is the primary attack vector on DES. Closing Comments After DES was deprecated and replaced by the Advanced Encryption Standard (AES) because of its vulnerability to a modestly-priced brute-force attack, many applications continued to rely on DES for security, and many software designers and implementers continued to include DES in new applications. In some cases, use of DES made sense but, inevitably, DES was discontinued in production software and hardware. RFC 4772 — dated December 2006 — discusses the security implications of employing DES, five years after AES had become the official standard. On a final note, readers may be interested in seeing an Excel implementation of DES or J.O. Grabbe's The DES Algorithm Illustrated. 5.5. Pretty Good Privacy (PGP)Pretty Good Privacy (PGP) is one of today's most widely used public key cryptography programs and was the first open cryptosystem that combined hashing, compression, SKC, and PKC into a method to protect files, devices, and e-mail. Public keys were shared via a concept known as a Web of Trust; individuals would directly exchange their public keyrings and then share their keyrings with other trusted parties. Developed by Philip Zimmermann in the early 1990s, and the subject of controversy for many years, PGP is available as a plug-in for many e-mail clients, such as Apple Mail (with GPG), Eudora, Gmail, Microsoft Outlook/Outlook Express, Mozilla Thunderbird (with Enigmail), and ProtonMail.
PGP can be used to sign or encrypt e-mail messages with the mere click of the mouse. Depending upon the version of PGP, the software uses SHA or MD5 for calculating the message hash; CAST, Triple-DES, or IDEA for encryption; and RSA or DSS/Diffie-Hellman for key exchange and digital signatures. When PGP is first installed, the user has to create a key-pair. One key, the public key, can be advertised and widely circulated. The private key is protected by use of a passphrase. The passphrase has to be entered every time the user accesses their private key. -----BEGIN PGP SIGNED MESSAGE----- Hash: SHA512 Hi Carol. What was that pithy Groucho Marx quote? /kess -----BEGIN PGP SIGNATURE----- Comment: GPGTools - https://gpgtools.org iQEcBAEBCgAGBQJYaTDaAAoJEE2ePRsA5fMj9wcH/jje/RBQYKg1ZYq1h52FpS3f GqnIkKq0wv2KiyCqIilbvb8eo2Fit7sIRo5AO3FJ9qIgRHvet+8pnRboks3uTYTM euNctkTOxcECZHupexdfB/5j5kGLn8UytIpHMa/Th4LKqvh+a6fU4nlCXe1qRSDq 7HUAvtG03LhPoAoVS411+wI+UtUf1+xvHLRJeKnhgi5j/d9tbc+K5rhPr8Bqb4Kz oHkGauPffRPfTsS+YpNoxg4eXMPBJprS9va8L2lCBPyUYEW77SSX/H2FHqPjVaxx /7j39Eu/oYtt5axnFBCYMZ2680kkFycd1RnCqhRJ8KZs6zhv3B8nQp6iS9dXrhg= =+mjr -----END PGP SIGNATURE----- FIGURE 12: A PGP signed message. The sender uses their private key to sign the message; at the destination, the sender's e-mail address yields the public key from the receiver's keyring in order to validate the signature. Figure 12 shows a PGP signed message. This message will not be kept secret from an eavesdropper, but a recipient can be assured that the message has not been altered from what the sender transmitted. In this instance, the sender signs the message using their own private key. The receiver uses the sender's public key to verify the signature; the public key is taken from the receiver's keyring based on the sender's e-mail address. Note that the signature process does not work unless the sender's public key is on the receiver's keyring. -----BEGIN PGP MESSAGE----- Comment: GPGTools - https://gpgtools.org hQEMA02ePRsA5fMjAQf/fJIFvXKggtfaSAXJzRRZ3sXhKJN+0kH5Kj7GdqbhBd81 n0TZ31BAoXksEQ0Q3HbN8PbJ4qTwLE+glAqVqaGfGmieEirD74/6jX/jffuA028+ X110IX4gJTpkhHzYeabrxPy9yerjI2EQL0XI4313K7w4vKZ8kAEVU86+DCHKm3br B/UrYlYDPg2xPjgqIx8Zyga2fSnb4TvqYs2+6k9O7RHKu72wKY0H/xx+rqhEmEAk L/sIxrlCufVM22zEnlbhO5BEqRhBN6CkRS7HkvxOWHetw4dOIbCjc1WI2CMGzHoK Lx2a3wOskjFbS+0PnDU/CKJV002fO+MCxvYhsF3B7dLAFAG80+08XFBKMll99/Wj bttk96NLkaz45SG9KNJyqj7KaRFYscnUbEjHunvFIJCnl0CblJb3J/gBaa/ZbSLq 0GGDr9oc0tKoR97mabkyAhohcpiIn7f2y2aCBx5qTRT2uMiedmu4XtyktgB4LUo+ /MspTWlbcyKk9+Gx+9a7QaRkvBskwDn1wL/EIfNhXvtga+qGCV3rZwEX7f46jdzi NcptK7urvqiWgYtKS1z/0VrppbHBoTux3TQcFAEzKAGCYnS2YCyjNJRqTC/ODPE8 BIIYcYNq =+eqR -----END PGP MESSAGE----- FIGURE 13: A PGP encrypted message. The receiver's e-mail address is the pointer to the public key in the sender's keyring with which to encrypt the message. At the destination side, the receiver uses their own private key to decrypt the message. Figure 13 shows a PGP encrypted message (PGP compresses the file, where practical, prior to encryption because encrypted files have a high degree of randomness and, therefore, cannot be efficiently compressed). In this example, public key methods are used to exchange the session key for the actual message encryption that employs secret-key cryptography. In this case, the receiver's e-mail address is the pointer to the public key in the sender's keyring; in fact, the same message can be sent to multiple recipients and the message will not be significantly longer since all that needs to be added is the session key encrypted by each receiver's public key. When the message is received, the recipient will use their private key to extract the session secret key to successfully decrypt the message (Figure 14). Hi Gary, "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." Carol FIGURE 14: The decrypted message. It is worth noting that PGP was one of the first so-called "hybrid cryptosystems" that combined aspects of SKC and PKC. When Zimmermann was first designing PGP in the late-1980s, he wanted to use RSA to encrypt the entire message. The PCs of the days, however, suffered significant performance degradation when executing RSA so he hit upon the idea of using SKC to encrypt the message and PKC to encrypt the SKC key. PGP went into a state of flux in 2002. Zimmermann sold PGP to Network Associates, Inc. (NAI) in 1997 and then resigned from NAI in early 2001. In March 2002, NAI announced that they were dropping support for the commercial version of PGP having failed to find a buyer for the product willing to pay what they wanted. In August 2002, PGP was purchased from NAI by PGP Corp. which, in turn, was purchased by Symantec. Meanwhile, there are many freeware versions of PGP available through the International PGP Page and the OpenPGP Alliance. OpenPGP is described more in RFC 4880. The open-source programming GNU (an acronym for "GNU's Not Unix") project has developed GnuPG, aka GPG. For additional information, see the GNU Privacy Guard (GnuPG) and GPGTools Web pages. 5.6. IP Security (IPsec) Protocol
The Internet and the TCP/IP protocol suite were not built with security in mind. This is not meant as a criticism but as an observation; the baseline IP, TCP, UDP, and ICMP protocols were written in 1980 and built for the relatively closed ARPANET community. TCP/IP wasn't designed for the commercial-grade financial transactions that they now see or for virtual private networks (VPNs) on the Internet. To bring TCP/IP up to today's security necessities, the Internet Engineering Task Force (IETF) formed the IP Security Protocol Working Group which, in turn, developed the IP Security (IPsec) protocol. IPsec is not a single protocol, in fact, but a suite of protocols providing a mechanism to provide data integrity, authentication, privacy, and nonrepudiation for the classic Internet Protocol (IP). Although intended primarily for IP version 6 (IPv6), IPsec can also be employed by the current version of IP, namely IP version 4 (IPv4). As shown in Table 3, IPsec is described in nearly a dozen RFCs. RFC 4301, in particular, describes the overall IP security architecture and RFC 2411 provides an overview of the IPsec protocol suite and the documents describing it. IPsec can provide either message authentication and/or encryption. The latter requires more processing than the former, but will probably end up being the preferred usage for applications such as VPNs and secure electronic commerce. Central to IPsec is the concept of a security association (SA). Authentication and confidentiality using AH or ESP use SAs and a primary role of IPsec key exchange it to establish and maintain SAs. An SA is a simplex (one-way or unidirectional) logical connection between two communicating IP endpoints that provides security services to the traffic carried by it using either AH or ESP procedures. The endpoint of an SA can be an IP host or IP security gateway (e.g., a proxy server, VPN server, etc.). Providing security to the more typical scenario of two-way (bi-directional) communication between two endpoints requires the establishment of two SAs (one in each direction). An SA is uniquely identified by a 3-tuple composed of:
The IP Authentication Header (AH), described in RFC 4302, provides a mechanism for data integrity and data origin authentication for IP packets using HMAC with MD5 (RFC 2403 and RFC 6151), HMAC with SHA-1 (RFC 2404), or HMAC with RIPEMD (RFC 2857). See also RFC 4305. 0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Next Header | Payload Len | RESERVED |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Security Parameters Index (SPI) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Sequence Number Field |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
+ Integrity Check Value-ICV (variable) |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
FIGURE 15: IPsec Authentication Header format. (From RFC 4302) Figure 15 shows the format of the IPsec AH. The AH is merely an additional header in a packet, more or less representing another protocol layer above IP (this is shown in Figure 17 below). Use of the IP AH is indicated by placing the value 51 (0x33) in the IPv4 Protocol or IPv6 Next Header field in the IP packet header. The AH follows mandatory IPv4/IPv6 header fields and precedes higher layer protocol (e.g., TCP, UDP) information. The contents of the AH are:
The IP Encapsulating Security Payload (ESP), described in RFC 4303, provides message integrity and privacy mechanisms in addition to authentication. As in AH, ESP uses HMAC with MD5, SHA-1, or RIPEMD authentication (RFC 2403/RFC 2404/RFC 2857); privacy is provided using DES-CBC encryption (RFC 2405), NULL encryption (RFC 2410), other CBC-mode algorithms (RFC 2451), or AES (RFC 3686). See also RFC 4305 and RFC 4308. 0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ ----
| Security Parameters Index (SPI) | ^Int.
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ |Cov-
| Sequence Number | |ered
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ | ----
| Payload Data* (variable) | | ^
~ ~ | |
| | |Conf.
+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ |Cov-
| | Padding (0-255 bytes) | |ered*
+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ | |
| | Pad Length | Next Header | v v
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ ------
| Integrity Check Value-ICV (variable) |
~ ~
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
* If included in the Payload field, cryptographic synchronization
data, e.g., an Initialization Vector (IV), usually is not
encrypted per se, although it often is referred to as being
being part of the ciphertext.
FIGURE 16: IPsec Encapsulating Security Payload format. (From RFC 4303) Figure 16 shows the format of the IPsec ESP information. Use of the IP ESP format is indicated by placing the value 50 (0x32) in the IPv4 Protocol or IPv6 Next Header field in the IP packet header. The ESP header (i.e., SPI and sequence number) follows mandatory IPv4/IPv6 header fields and precedes higher layer protocol (e.g., TCP, UDP) information. The contents of the ESP packet are:
Two types of SAs are defined in IPsec, regardless of whether AH or ESP is employed. A transport mode SA is a security association between two hosts. Transport mode provides the authentication and/or encryption service to the higher layer protocol. This mode of operation is only supported by IPsec hosts. A tunnel mode SA is a security association applied to an IP tunnel. In this mode, there is an "outer" IP header that specifies the IPsec destination and an "inner" IP header that specifies the destination for the IP packet. This mode of operation is supported by both hosts and security gateways. ORIGINAL PACKET BEFORE APPLYING AH
----------------------------
IPv4 |orig IP hdr | | |
|(any options)| TCP | Data |
----------------------------
---------------------------------------
IPv6 | | ext hdrs | | |
| orig IP hdr |if present| TCP | Data |
---------------------------------------
AFTER APPLYING AH (TRANSPORT MODE)
-------------------------------------------------------
IPv4 |original IP hdr (any options) | AH | TCP | Data |
-------------------------------------------------------
|<- mutable field processing ->|<- immutable fields ->|
|<----- authenticated except for mutable fields ----->|
------------------------------------------------------------
IPv6 | |hop-by-hop, dest*, | | dest | | |
|orig IP hdr |routing, fragment. | AH | opt* | TCP | Data |
------------------------------------------------------------
|<--- mutable field processing -->|<-- immutable fields -->|
|<---- authenticated except for mutable fields ----------->|
* = if present, could be before AH, after AH, or both
AFTER APPLYING AH (TUNNEL MODE)
----------------------------------------------------------------
IPv4 | | | orig IP hdr* | | |
|new IP header * (any options) | AH | (any options) |TCP| Data |
----------------------------------------------------------------
|<- mutable field processing ->|<------ immutable fields ----->|
|<- authenticated except for mutable fields in the new IP hdr->|
--------------------------------------------------------------
IPv6 | | ext hdrs*| | | ext hdrs*| | |
|new IP hdr*|if present| AH |orig IP hdr*|if present|TCP|Data|
--------------------------------------------------------------
|<--- mutable field -->|<--------- immutable fields -------->|
| processing |
|<-- authenticated except for mutable fields in new IP hdr ->|
* = if present, construction of outer IP hdr/extensions and
modification of inner IP hdr/extensions is discussed in
the Security Architecture document.
FIGURE 17: IPsec tunnel and transport modes for AH. (Adapted from RFC 4302) Figure 17 shows the IPv4 and IPv6 packet formats when using AH in both transport and tunnel modes. Initially, an IPv4 packet contains a normal IPv4 header (which may contain IP options), followed by the higher layer protocol header (e.g., TCP or UDP), followed by the higher layer data itself. An IPv6 packet is similar except that the packet starts with the mandatory IPv6 header followed by any IPv6 extension headers, and then followed by the higher layer data. Note that in both transport and tunnel modes, the entire IP packet is covered by the authentication except for the mutable fields. A field is mutable if its value might change during transit in the network; IPv4 mutable fields include the fragment offset, time to live, and checksum fields. Note, in particular, that the address fields are not mutable. ORIGINAL PACKET BEFORE APPLYING ESP
----------------------------
IPv4 |orig IP hdr | | |
|(any options)| TCP | Data |
----------------------------
---------------------------------------
IPv6 | | ext hdrs | | |
| orig IP hdr |if present| TCP | Data |
---------------------------------------
AFTER APPLYING ESP (TRANSPORT MODE)
-------------------------------------------------
IPv4 |orig IP hdr | ESP | | | ESP | ESP|
|(any options)| Hdr | TCP | Data | Trailer | ICV|
-------------------------------------------------
|<---- encryption ---->|
|<-------- integrity ------->|
---------------------------------------------------------
IPv6 | orig |hop-by-hop,dest*,| |dest| | | ESP | ESP|
|IP hdr|routing,fragment.|ESP|opt*|TCP|Data|Trailer| ICV|
---------------------------------------------------------
|<--- encryption ---->|
|<------ integrity ------>|
* = if present, could be before ESP, after ESP, or both
AFTER APPLYING ESP (TUNNEL MODE)
-----------------------------------------------------------
IPv4 | new IP hdr+ | | orig IP hdr+ | | | ESP | ESP|
|(any options)| ESP | (any options) |TCP|Data|Trailer| ICV|
-----------------------------------------------------------
|<--------- encryption --------->|
|<------------- integrity ------------>|
------------------------------------------------------------
IPv6 | new+ |new ext | | orig+|orig ext | | | ESP | ESP|
|IP hdr| hdrs+ |ESP|IP hdr| hdrs+ |TCP|Data|Trailer| ICV|
------------------------------------------------------------
|<--------- encryption ---------->|
|<------------ integrity ------------>|
+ = if present, construction of outer IP hdr/extensions and
modification of inner IP hdr/extensions is discussed in
the Security Architecture document.
FIGURE 18: IPsec tunnel and transport modes for ESP. (Adapted from RFC 4303) Figure 18 shows the IPv4 and IPv6 packet formats when using ESP in both transport and tunnel modes.
Note a significant difference in the scope of ESP and AH. AH authenticates the entire packet transmitted on the network whereas ESP only covers a portion of the packet transmitted on the network (the higher layer data in transport mode and the entire original packet in tunnel mode). The reason for this is straight-forward; in AH, the authentication data for the transmission fits neatly into an additional header whereas ESP creates an entirely new packet which is the one encrypted and/or authenticated. But the ramifications are significant. ESP transport mode as well as AH in both modes protect the IP address fields of the original transmissions. Thus, using IPsec in conjunction with network address translation (NAT) might be problematic because NAT changes the values of these fields after IPsec processing. The third component of IPsec is the establishment of security associations and key management. These tasks can be accomplished in one of two ways. The simplest form of SA and key management is manual management. In this method, a security administer or other individual manually configures each system with the key and SA management data necessary for secure communication with other systems. Manual techniques are practical for small, reasonably static environments but they do not scale well. For successful deployment of IPsec, however, a scalable, automated SA/key management scheme is necessary. Several protocols have defined for these functions:
5.7. Secure Transactions with SSL and TLSThe Secure Sockets Layer (SSL) protocol was developed by Netscape Communications to provide application-independent secure communication over the Internet for protocols such as the Hypertext Transfer Protocol (HTTP). SSL employs RSA and X.509 certificates during an initial handshake used to authenticate the server (client authentication is optional). The client and server then agree upon an encryption scheme. SSL v2.0 (1995), the first version publicly released, supported RC2 and RC4 with 40-bit keys. SSL v3.0 (1996) added support for DES, RC4 with a 128-bit key, and 3DES with a 168-bit key, all along with either MD5 or SHA-1 message hashes; this protocol is described in RFC 6101.
FIGURE 19: Browser encryption configuration screen (Firefox). In 1997, SSL v3 was found to be breakable. By this time, the Internet Engineering Task Force (IETF) had already started work on a new, non-proprietary protocol called Transport Layer Security (TLS), described in RFC 2246 (1999). TLS extends SSL and supports additional crypto schemes, such as Diffie-Hellman key exchange and DSS digital signatures; RFC 4279 describes the pre-shared key crypto schemes supported by TLS. TLS is backward compatible with SSL (and, in fact, is recognized as SSL v3.1). SSL v3.0 and TLS v1.0 are the commonly supported versions on servers and browsers today (Figure 19); SSL v2.0 is rarely found today and, in fact, RFC 6176-compliant clients and servers that support TLS will never negotiate the use of SSL v2. In 2002, a cipher block chaining (CBC) vulnerability was described for TLS v1.0. In 2011, the theoretical became practical when a CBC proof-of-concept exploit was released. Meanwhile, TLS v1.1 was defined in 2006 (RFC 4346), adding protection against v1.0's CBC vulnerability. In 2008, TLS v1.2 was defined (RFC 5246), adding several additional cryptographic options. In 2018, TLS v1.3 was introduced (RFC 8446), adding clarification of acceptable crypto methods and better security. Client Server
Key ^ ClientHello
Exch | + key_share*
| + signature_algorithms*
| + psk_key_exchange_modes*
v + pre_shared_key* -------->
ServerHello ^ Key
+ key_share* | Exch
+ pre_shared_key* v
{EncryptedExtensions} ^ Server
{CertificateRequest*} v Params
{Certificate*} ^
{CertificateVerify*} | Auth
{Finished} v
<-------- [Application Data*]
^ {Certificate*}
Auth | {CertificateVerify*}
v {Finished} -------->
[Application Data] <-------> [Application Data]
+ Indicates noteworthy extensions sent in the previously noted message.
* Indicates optional or situation-dependent messages/extensions that are not always sent.
{} Indicates messages protected using keys derived from a [sender]_handshake_traffic_secret.
[] Indicates messages protected using keys derived from [sender]_application_traffic_secret_N.
FIGURE 20: Basic TLS protocol handshake. (From RFC 8446)The use of TLS is initiated when a user specifies the protocol https:// in a URL. The client (i.e., browser) will automatically try to make a TCP connection to the server at port 443 (unless another port is specified in the URL). The communication between the client and server comprises the TLS protocol handshake (Figure 20), which has three phases, followed by actual data exchange. The first phase of the protocol handshake is Key Exchange, used to establish the shared key and select the encryption method. This is the only phase of TLS communication that is not encrypted. During this phase:
From this point forward, all communication is encrypted. The second step of the protocol handshake is the Server Parameters phase, where the server specifies other, additional handshake parameters. The server accomplishes this task by the use of two messages:
The third, and final phase, of the TLS protocol handshake is Authentication, during which the server is authenticated (and, optionally, the client), keys are confirmed, and the integrity of the handshake assured. The messages exchanged during this phase include:
During this phase, the server sends its authentication messages followed by the client sending its authentication messages. Once the Finished messages have been exchanged, the protocol handshake is complete, and the client and server now start to exchange encrypted Application Data. Side Note: It would probably be helpful to make some mention of how SSL/TLS is most commonly used today. Most of us have used SSL to engage in a secure, private transaction with some vendor. The steps are something like this. During the SSL exchange with the vendor's secure server, the server sends its certificate to our client software. The certificate includes the vendor's public key and a validation of some sort from the CA that issued the vendor's certificate (signed with the CA's private key). Our browser software is shipped with the major CAs' certificates containing their public keys; in that way, the client software can authenticate the server's certificate. Note that the server generally does not use a certificate to authenticate the client. Instead, purchasers are generally authenticated when a credit card number is provided; the server checks to see if the card purchase will be authorized by the credit card company and, if so, considers us valid and authenticated! The reason that only the server is authenticated is rooted in history. SSL was developed to support e-commerce by providing a trust mechanism so that customers could have faith in a merchant. In the real world, you "trust" a store because you can walk into a brick-and-mortar structure. The store doesn't know who the customer is; they check to see if the credit card is valid and, if so, a purchase goes through. In e-commerce, we were trying to replicate the same experience — find a way in which the customer could trust the store and then make sure that the credit card was valid. In addition, how many people would have been willing to purchase an individual certificate and install it on their browser merely so that they shop online? This latter requirement, if implemented, could have killed e-commerce before it ever got started. This all said, bidirectional — or mutual — authentication is supported by SSL, as noted in the figure above. See E. Cheng's "An Introduction to Mutual SSL Authentication" for an overview of how symmetric the process can be. For historical purposes, it is worth mentioning Microsoft's Server Gated Cryptography (SGC) protocol, another (now long defunct) extension to SSL/TLS. For several decades, it had been illegal to generally export products from the U.S. that employed secret-key cryptography with keys longer than 40 bits. For that reason, during the 1996-1998 time period, browsers using SSL/TLS (e.g., Internet Explorer and Netscape Navigator) had an exportable version with weak (40-bit) keys and a domestic (North American) version with strong (128-bit) keys. By the late-1990s, products using strong SKC has been approved for the worldwide financial community. SGC was an extension to SSL that allowed financial institutions using Windows NT servers to employ strong cryptography. Both the client and server needed to have implemented SGC and the bank had to have a valid SGC certificate. During the initial handshake, the server would indicate support of SGC and supply its SGC certificate; if the client wished to use SGC and validated the server's SGC certificate, it would establish a secure session employing 128-bit RC2, 128-bit RC4, 56-bit DES, or 168-bit 3DES encryption. Microsoft supported SGC in the Windows 95/98/NT versions of Internet Explorer 4.0, Internet Information Server (IIS) 4.0, and Money 98. As mentioned earlier, SSL was designed to provide application-independent transaction security for the Internet. Although the discussion above has focused on HTTP over SSL (https/TCP port 443), SSL can be used with several TCP/IP protocols (Table 4). TABLE 4. Internet protocols over SSL.
TLS was originally designed to operate over TCP. The IETF developed the Datagram Transport Layer Security (DTLS) protocol, based upon TLS, to operate over UDP. DTLS v1.3 is described in RFC 9147. (RFC 6347 defines DTLS v1.2 and DTLS v1.0 can be found in RFC 4347.) RFC 6655 describes a suite of AES in Counter with Cipher Block Chaining - Message Authentication Code (CBC-MAC) Mode (CCM) ciphers for use with TLS and DTLS. An interesting analysis of the TLS protocol can be found in the paper "Analysis and Processing of Cryptographic Protocols" by Cowie. Vulnerabilities: A vulnerability in the OpenSSL Library was discovered in 2014. Known as Heartbleed, this vulnerability had apparently been introduced into OpenSSL in late 2011 with the introduction of a feature called heartbeat. Heartbleed exploited an implementation flaw in order to exfiltrate keying material from an SSL server (or some SSL clients, in what is known at reverse Heartbleed); the flaw allowed an attacker to grab 64 KB blocks from RAM. Heartbleed is known to only affect OpenSSL v1.0.1 through v1.0.1f; the exploit was patched in v1.0.1g. In addition, the OpenSSL 0.9.8 and 1.0.0 families are not vulnerable. Note also that Heartbleed affects some versions of the Android operating system, notably v4.1.0 and v4.1.1 (and some, possibly custom, implementations of v4.2.2). Note that Heartbleed did not exploit a flaw in the SSL protocol, but rather a flaw in the OpenSSL implementation. But that wasn't the only problem with SSL. In October 2014, a new vulnerability was found called POODLE (Padding Oracle On Downgraded Legacy Encryption), a man-in-the-middle attack that exploited another SSL vulnerability that had unknowingly been in place for many years. Weeks later, an SSL vulnerability in the bash Unix command shell was discovered, aptly named Shellshock. (Here's a nice overview of the 2014 SSL problems!) In March 2015, the Bar Mitzvah Attack was exposed, exploiting a 13-year old vulnerability in the Rivest Cipher 4 (RC4) encryption algorithm. Then there was the FREAK (Factoring Attack on RSA-EXPORT Keys CVE-2015-0204) SSL/TLS Vulnerability that affected some SSL/TLS implementations, including Android OS and Chrome browser for OS X later that month. In March 2016, the SSL DROWN (Decrypting RSA with Obsolete and Weakened eNcryption) attack was announced. DROWN works by exploiting the presence of SSLv2 to crack encrypted communications and steal information from Web servers, email servers, or VPN sessions. You might have read above that SSLv2 fell out of use by the early 2000s and was formally deprecated in 2011. This is true. But backward compatibility often causes old software to remain dormant and it seems that up to one-third of all HTTPS sites at the time were vulnerable to DROWN because SSLv2 had not been removed or disabled. 5.8. Elliptic Curve Cryptography (ECC)In general, public key cryptography systems use hard-to-solve problems as the basis of the algorithm. The most predominant public key cryptography algorithm for many years was RSA, based on the prime factors of very large integers. While RSA can be successfully attacked, the mathematics of the algorithm have not been compromised, per se; instead, computational brute-force has broken the keys. The defense is "simple" — keep the size of the integer to be factored ahead of the computational curve! In 1985, Elliptic Curve Cryptography (ECC) was proposed independently by cryptographers Victor Miller (IBM) and Neal Koblitz (University of Washington). ECC is based on the difficulty of solving the Elliptic Curve Discrete Logarithm Problem (ECDLP). Like the prime factorization problem, ECDLP is another "hard" problem that is deceptively simple to state: Given two points, P and Q, on an elliptic curve, find the integer n, if it exists, such that Q = nP. The first thing to note about elliptic curves is that they are neither elliptic (i.e., they are not an oval or ellipse) nor are they curves (i.e., they are not curves in common meaning, which are merely bent lines). Elliptic curves are a part of number theory and algebraic geometry, and can be defined over any field of numbers (i.e., real, integer, complex, etc.). In cryptography, we normally use elliptic curves over a finite field of prime numbers, which we denote FP. This is one reason that we use the modulo function; modulo arithmetic defines a finite range of numbers (e.g., 0 to N-1 if using modulo N) which will, in turn, yield a finite number of primes. So, given this preamble, an elliptic curve in FP consists of the set of real numbers (x,y) that satisfies the equation: y2 = (x3 + ax + b) modulo N In addition, the curve has to be non-singular (sometimes stated as "not containing any singularities"), which means that the curve has no cusps, self-intersections, or isolated points. To ensure this, there is one more condition, namely, the values of a and b must satisfy the requirement that: 4a3 + 27b2 ≠ 0 The set of all of the solutions to the equation forms the elliptic curve. Changing a and b changes the shape of the curve, and small changes in these parameters can result in major changes in the set of (x,y) solutions. The ECC standards documents list a host of ECC curves and they differ by changing these parameters.
FIGURE 21: Elliptic curve addition. (Source: Dams, 2012) Figure 21 shows the addition of two points on the elliptic curve where a = -3 and b = 5. Elliptic curves have the interesting property that adding two points on the elliptic curve yields a third point on the curve. Therefore, adding two points, P and Q, gets us to point R. Small changes in P or Q can cause a large change in the position of R. Now, the astute reader will notice that the line above went through a point labelled -R and that, in the Cartesian coordinate system, we've merely changed the sign of the y coordinate to get the point labelled R; i.e., we've "reflected" the point around the x-axis. It turns out that it doesn't matter because the curve is solving the equation for y2, meaning that if a point exists in the +y space, the same point exists in the -y space because (+y)2 = (-y)2. Stated another, slightly more rigorous way, the curve is symmetric about the x-axis. Meanwhile, if it doesn't matter, why do it? Remember that our original problem was to find Q = nP. So, to get there, we need to define a number of operations on P, including doubling P and multiplying P by some number. At this point, we leave the area of simple scalar arithmetic and enter into group law and algebraic geometry. There are a bunch of good explanations about why we do this reflection that I am not going to replicate but I will give one key thing to keep in mind. While the sign doesn't matter when squaring a number, it does matter in other types of arithmetic. When adding points on the elliptic curve, we need to maintain the associative law, which says: (A + B) + C = A + (B + C) Working with elliptic curves gets us into group laws and the operations often reflect about the x-axis in order to maintain the associative principle. In any case, there's a pretty good discussion about this on StackExchange and in "The group law" section on the ECC Wikipedia page. So let's go back to the original problem statement from above. The point Q is calculated as a multiple of the starting point, P, or, Q = nP. An attacker might know P and Q but finding the integer, n, is a difficult problem to solve. Q (i.e., nP) is the public key and n is the private key. ECC may be employed with many Internet standards, including CCITT X.509 certificates and certificate revocation lists (CRLs), Internet Key Exchange (IKE), Transport Layer Security (TLS), XML signatures, and applications or protocols based on the cryptographic message syntax (CMS). ANSI, IEEE, IETF, NIST, the Standards for Efficient Cryptography Group (SECG), and others have also defined "safe curves" for use in various applications for ECC, such as:
See Bernstein and Lange's SafeCurves: choosing safe curves for elliptic-curve cryptography site for a review and analysis of various ECC curve standard specifications. TABLE 5. ECC and RSA Key Comparison, and Equivalent AES Key Size. (Source: Certicom, NIST)
RSA had been the mainstay of PKC since its development in the late 1970s. ECC has emerged as a replacement in many environments because it provides similar levels of security compared to RSA but with significantly reduced key sizes and, therefore, reduced processing demands. Table 5 shows the key size relationship between ECC and RSA, and the appropriate choice of AES key size. Since the ECC key sizes are so much shorter than comparable RSA keys, the length of the public key and private key is much shorter in elliptic curve cryptosystems. This results into faster processing times, and lower demands on memory and bandwidth; some studies have found that ECC is faster than RSA for signing and decryption, but slower for signature verification and encryption. ECC is particularly useful in applications where memory, bandwidth, and/or computational power is limited (e.g., a smartcard or smart device) and it is in this area that ECC use has been growing. There are a number of exceptional ECC tutorials online at various levels of detail and complexity to which readers are referred:
5.9. The Advanced Encryption Standard (AES) and RijndaelThe search for a replacement to DES started in January 1997 when NIST announced that it was looking for an Advanced Encryption Standard. In September of that year, they put out a formal Call for Algorithms and in August 1998 announced that 15 candidate algorithms were being considered (Round 1). In April 1999, NIST announced that the 15 had been whittled down to five finalists (Round 2): MARS (multiplication, addition, rotation and substitution) from IBM; Ronald Rivest's RC6; Rijndael from a Belgian team; Serpent, developed jointly by a team from England, Israel, and Norway; and Twofish, developed by Bruce Schneier. In October 2000, NIST announced their selection: Rijndael. The remarkable thing about this entire process has been the openness as well as the international nature of the "competition." NIST maintained an excellent Web site devoted to keeping the public fully informed, at http://csrc.nist.gov/archive/aes/, which is now available as an archive site. Their Overview of the AES Development Effort has full details of the process, algorithms, and comments so I will not repeat everything here. In October 2000, NIST released the Report on the Development of the Advanced Encryption Standard (AES) that compared the five Round 2 algorithms in a number of categories. Table 6 summarizes the relative scores of the five schemes (1=low, 3=high): TABLE 6. Scores of AES Round 2 algorithms.
With the report came the recommendation that Rijndael be named as the AES standard. In February 2001, NIST released the Draft Federal Information Processing Standard (FIPS) AES Specification for public review and comment. AES contains a subset of Rijndael's capabilities (e.g., AES only supports a 128-bit block size) and uses some slightly different nomenclature and terminology, but to understand one is to understand both. The 90-day comment period ended on May 29, 2001 and the U.S. Department of Commerce officially adopted AES in December 2001, published as FIPS PUB 197. AES (Rijndael) Overview Rijndael (pronounced as in "rain doll" or "rhine dahl") is a block cipher designed by Joan Daemen and Vincent Rijmen, both cryptographers in Belgium. Rijndael can operate over a variable-length block using variable-length keys; the specification submitted to NIST describes use of a 128-, 192-, or 256-bit key to encrypt data blocks that are 128, 192, or 256 bits long; note that all nine combinations of key length and block length are possible. The algorithm is written in such a way that block length and/or key length can easily be extended in multiples of 32 bits and it is specifically designed for efficient implementation in hardware or software on a range of processors. The design of Rijndael was strongly influenced by the block cipher called Square, also designed by Daemen and Rijmen. Rijndael is an iterated block cipher, meaning that the initial input block and cipher key undergoes multiple rounds of transformation before producing the output. Each intermediate cipher result is called a State. For ease of description, the block and cipher key are often represented as an array of columns where each array has 4 rows and each column represents a single byte (8 bits). The number of columns in an array representing the state or cipher key, then, can be calculated as the block or key length divided by 32 (32 bits = 4 bytes). An array representing a State will have Nb columns, where Nb values of 4, 6, and 8 correspond to a 128-, 192-, and 256-bit block, respectively. Similarly, an array representing a Cipher Key will have Nk columns, where Nk values of 4, 6, and 8 correspond to a 128-, 192-, and 256-bit key, respectively. An example of a 128-bit State (Nb=4) and 192-bit Cipher Key (Nk=6) is shown below:
The number of transformation rounds (Nr) in Rijndael is a function of the block length and key length, and is shown in Table 7. TABLE 7. Number of transformation rounds in Rijndael.
Now, having said all of this, the AES version of Rijndael does not support all nine combinations of block and key lengths, but only the subset using a 128-bit block size. NIST calls these supported variants AES-128, AES-192, and AES-256 where the number refers to the key size. Table 8 shows the Nb, Nk, and Nr values supported in AES. TABLE 8. Rijndael parameters supported in AES.
The AES/Rijndael cipher itself has three operational stages:
The paragraphs below will describe the operations mentioned above. The nomenclature used below is taken from the AES specification although references to the Rijndael specification are made for completeness. The arrays s and s' refer to the State before and after a transformation, respectively (NOTE: The Rijndael specification uses the array nomenclature a and b to refer to the before and after States, respectively). The subscripts i and j are used to indicate byte locations within the State (or Cipher Key) array. The SubBytes transformation The substitute bytes (called ByteSub in Rijndael) transformation operates on each of the State bytes independently and changes the byte value. An S-box, or substitution table, controls the transformation. The characteristics of the S-box transformation as well as a compliant S-box table are provided in the AES specification; as an example, an input State byte value of 107 (0x6b) will be replaced with a 127 (0x7f) in the output State and an input value of 8 (0x08) would be replaced with a 48 (0x30). One way to think of the SubBytes transformation is that a given byte in State s is given a new value in State s' according to the S-box. The S-box, then, is a function on a byte in State s so that: s'i,j = S-box (si,j) The more general depiction of this transformation is shown by:
The ShiftRows transformation The shift rows (called ShiftRow in Rijndael) transformation cyclically shifts the bytes in the bottom three rows of the State array. According to the more general Rijndael specification, rows 2, 3, and 4 are cyclically left-shifted by C1, C2, and C3 bytes, respectively, as shown below:
The current version of AES, of course, only allows a block size of 128 bits (Nb = 4) so that C1=1, C2=2, and C3=3. The diagram below shows the effect of the ShiftRows transformation on State s:
The MixColumns transformation The mix columns (called MixColumn in Rijndael) transformation uses a mathematical function to transform the values of a given column within a State, acting on the four values at one time as if they represented a four-term polynomial. In essence, if you think of MixColumns as a function, this could be written: s'i,c = MixColumns (si,c) for 0 ≤ i ≤ 3 for some column, c. The column position doesn't change, merely the values within the column. Round Key generation and the AddRoundKey transformation The AES Cipher Key can be 128, 192, or 256 bits in length. The Cipher Key is used to derive a different key to be applied to the block during each round of the encryption operation. These keys are called the Round Keys and each will be the same length as the block, i.e., Nb 32-bit words (words will be denoted W). The AES specification defines a key schedule by which the original Cipher Key (of length Nk 32-bit words) is used to form an Expanded Key. The Expanded Key size is equal to the block size times the number of encryption rounds plus 1, which will provide Nr+1 different keys. (Note that there are Nr encipherment rounds but Nr+1 AddRoundKey transformations.) Consider that AES uses a 128-bit block and either 10, 12, or 14 iterative rounds depending upon key length. With a 128-bit key, for example, we would need 1408 bits of key material (128x11=1408), or an Expanded Key size of 44 32-bit words (44x32=1408). Similarly, a 192-bit key would require 1664 bits of key material (128x13), or 52 32-bit words, while a 256-bit key would require 1920 bits of key material (128x15), or 60 32-bit words. The key expansion mechanism, then, starts with the 128-, 192-, or 256-bit Cipher Key and produces a 1408-, 1664-, or 1920-bit Expanded Key, respectively. The original Cipher Key occupies the first portion of the Expanded Key and is used to produce the remaining new key material. The result is an Expanded Key that can be thought of and used as 11, 13, or 15 separate keys, each used for one AddRoundKey operation. These, then, are the Round Keys. The diagram below shows an example using a 192-bit Cipher Key (Nk=6), shown in magenta italics:
The AddRoundKey (called Round Key addition in Rijndael) transformation merely applies each Round Key, in turn, to the State by a simple bit-wise exclusive OR operation. Recall that each Round Key is the same length as the block. Summary Ok, I hope that you've enjoyed reading this as much as I've enjoyed writing it — and now let me guide you out of the microdetail! Recall from the beginning of the AES overview that the cipher itself comprises a number of rounds of just a few functions:
Cipher (byte in[4*Nb], byte out[4*Nb], word w[Nb*(Nr+1)])
begin
byte state[4,Nb]
state = in
AddRoundKey(state, w)
for round = 1 step 1 to Nr-1
SubBytes(state)
ShiftRows(state)
MixColumns(state)
AddRoundKey(state, w+round*Nb)
end for
SubBytes(state)
ShiftRows(state)
AddRoundKey(state, w+Nr*Nb)
out = state
end
FIGURE 22: AES pseudocode.As a last and final demonstration of the operation of AES, Figure 22 is a pseudocode listing for the operation of the AES cipher. In the code:
5.10. Cisco's Stream CipherStream ciphers take advantage of the fact that: x ⊕ y ⊕ y = x One of the encryption schemes employed by Cisco routers to encrypt passwords is a stream cipher. It uses the following fixed keystream (thanks also to Jason Fossen for independently extending and confirming this string): dsfd;kfoA,.iyewrkldJKDHSUBsgvca69834ncx When a password is to be encrypted, the password function chooses a number between 0 and 15, and that becomes the offset into the keystream. Password characters are then XORed byte-by-byte with the keystream according to: Ci = Pi ⊕ K(offset+i) where K is the keystream, P is the plaintext password, and C is the ciphertext password. Consider the following example. Suppose we have the password abcdefgh. Converting the ASCII characters yields the hex string 0x6162636465666768. The keystream characters and hex code that supports an offset from 0 to 15 bytes and a password length up to 24 bytes is: d s f d ; k f o A , . i y e w r k l d J K D H S U B s g v c a 6 9 8 3 4 n c x Let's say that the function decides upon a keystream offset of 6 bytes. We then start with byte 6 of the keystream (start counting the offset at 0) and XOR with the password: 0x666f412c2e697965 The password would now be displayed in the router configuration as: password 7 06070D22484B0F1E0D where the "7" indicates the encryption type, the leading "06" indicates the offset into the keystream, and the remaining bytes are the encrypted password characters. (Decryption is pretty trivial so that exercise is left to the reader. If you need some help with byte-wise XORing, see http://www.garykessler.net/library/byte_logic_table.html. If you'd like some programs that do this, see http://www.garykessler.net/software/index.html#cisco7.) 5.11. TrueCryptTrueCrypt is an open source, on-the-fly crypto system that can be used on devices supports by Linux, MacOS, and Windows. First released in 2004, TrueCrypt can be employed to encrypt a partition on a disk or an entire disk.
TrueCrypt uses a variety of encryption schemes, including AES, Serpent, and Twofish. A TrueCrypt volume is stored as a file that appears to be filled with random data, thus has no specific file signature. (It is true that a TrueCrypt container will pass a chi-square (Χ2) randomness test, but that is merely a general indicator of possibly encrypted content. An additional clue is that a TrueCrypt container will also appear on a disk as a file that is some increment of 512 bytes in size. While these indicators might raise a red flag, they don't rise to the level of clearly identifying a TrueCrypt volume.) When a user creates a TrueCrypt volume, a number of parameters need to be defined, such as the size of the volume and the password. To access the volume, the TrueCrypt program is employed to find the TrueCrypt encrypted file, which is then mounted as a new drive on the host system.
FIGURE 23: TrueCrypt screen shot (Windows).
FIGURE 24: TrueCrypt screen shot (MacOS). Consider this example where an encrypted TrueCrypt volume is stored as a file named James on a thumb drive. On a Windows system, this thumb drive has been mounted as device E:. If one were to view the E: device, any number of files might be found. The TrueCrypt application is used to mount the TrueCrypt file; in this case, the user has chosen to mount the TrueCrypt volume as device K: (Figure 23). Alternatively, the thumb drive could be used with a Mac system, where it has been mounted as the /Volumes/JIMMY volume. TrueCrypt mounts the encrypted file, James, and it is now accessible to the system (Figure 24). FIGURE 25: TrueCrypt hidden encrypted volume within an encrypted volume. (From http://www.truecrypt.org/images/docs/hidden-volume.gif) One of the most interesting — certainly one of the most controversial — features of TrueCrypt is called plausible deniability, protection in case a user is "compelled" to turn over the encrypted volume's password. When the user creates a TrueCrypt volume, he/she chooses whether to create a standard or hidden volume. A standard volume has a single password, while a hidden volume is created within a standard volume and uses a second password. As shown in Figure 25, the unallocated (free) space in a TrueCrypt volume is always filled with random data, thus it is impossible to differentiate a hidden encrypted volume from a standard volume's free space. To access the hidden volume, the file is mounted as shown above and the user enters the hidden volume's password. When under duress, the user would merely enter the password of the standard (i.e., non-hidden) TrueCrypt volume. More information about TrueCrypt can be found at the TCnext Web Site or in the TrueCrypt User's Guide (v7.1a).
5.12. Encrypting File System (EFS)Microsoft introduced the Encrypting File System (EFS) with the NTFS v3.0 file system and has supported EFS since Windows 2000 and XP (although EFS was and is not supported in all variations of Windows). Since Windows 10, EFS can also be used on FAT and exFAT volumes. EFS can be used to encrypt individual files, directories, or entire volumes. While disabled by default, EFS encryption can be easily enabled via File Explorer (aka Windows Explorer) by right-clicking on the file, directory, or volume to be encrypted, selecting Properties, Advanced, and Encrypt contents to secure data (Figure 26). Note that encrypted files and directories are displayed in green in Windows Explorer.
FIGURE 26: EFS and Windows (File) Explorer. The Windows command prompt provides an easy tool with which to detect EFS-encrypted files on a disk. The cipher command has a number of options, but the /u/n switches can be used to list all encrypted files on a drive (Figure 27).
FIGURE 27: The cipher command. EFS supports a variety of secret key encryption schemes, including 3DES, DESX, AES, and ECC, as well as RSA public key encryption. The operation of EFS — at least at the theoretical level — is relatively straight-forward. When a file is saved to disk:
When the file is opened:
There are weaknesses with the system, most of which are related to key management. As an example, the RSA private key can be stored on an external device such as a floppy disk (yes, really!), thumb drive, or smart card. In practice, however, this is rarely done; the user's private RSA key is often stored on the hard drive. In addition, early EFS implementations (prior to Windows XP SP2) tied the key to the username; later implementations employ the user's password. A more serious implementation issue is that a backup file named esf0.tmp is created prior to a file being encrypted. After the encryption operation, the backup file is deleted — not wiped — leaving an unencrypted version of the file available to be undeleted. For this reason, it is best to use encrypted directories because the temporary backup file is protected by being in an encrypted directory.
FIGURE 28: EFS key storage. (Source: NTFS.com) The EFS information is stored as a named stream in the $LOGGED_UTILITY_STREAM Attribute (attribute type 256 [0x100]). This information includes (Figure 28):
Master File Table (MFT) Parser V2.1 - Gary C. Kessler (11 June 2013) : : 0056-0059 Attribute type: 0x10-00-00-00 [$STANDARD_INFORMATION] 0060-0063 Attribute length: 0x60-00-00-00 [96 bytes] 0064 Non-resident flag: 0x00 [Attribute is resident] : : 0152-0155 Attribute type: 0x30-00-00-00 [$FILE_NAME] 0156-0159 Attribute length: 0x70-00-00-00 [112 bytes] 0160 Non-resident flag: 0x00 [Attribute is resident] : : 0264-0267 Attribute type: 0x40-00-00-00 [$VOLUME_VERSION/$OBJECT_ID] 0268-0271 Attribute length: 0x28-00-00-00 [40 bytes] 0272 Non-resident flag: 0x00 [Attribute is resident] : : 0304-0307 Attribute type: 0x80-00-00-00 [$DATA] 0308-0311 Attribute length: 0x48-00-00-00 [72 bytes] 0312 Non-resident flag: 0x01 [Attribute is non-resident] 0313 Name length: 0x00 [0 16-bit characters] 0314-0315 Offset to name: 0x00-00 [0 bytes] 0316-0317 Flag: 0x00-40 -- Encrypted : : 0376-0379 Attribute type: 0x00-01-00-00 [$LOGGED_UTILITY_STREAM] 0380-0383 Attribute length: 0x50-00-00-00 [80 bytes] 0384 Non-resident flag: 0x01 [Attribute is non-resident] : 0440-0447 Name: 0x24-00-45-00-46-00-53-00 [$EFS] : : FIGURE 29: The $LOGGED_UTILITY_STREAM Attribute (see complete output at crypto_EFS.txt). Files in an NTFS file system maintain a number of attributes that contain the system metadata (e.g., the $STANDARD_INFORMATION attribute maintains the file timestamps and the $FILE_NAME attribute contains the file name). Files encrypted with EFS store the keys, as stated above, in a data stream named $EFS within the $LOGGED_UTILITY_STREAM attribute. Figure 29 shows the partial contents of the Master File Table (MFT) attributes for an EFS encrypted file. 5.13. Some of the Finer Details of RC4RC4 is a variable key-sized stream cipher developed by Ron Rivest in 1987. RC4 works in output-feedback (OFB) mode, so that the key stream is independent of the plaintext. The algorithm is described in detail in Schneier's Applied Cryptography, 2/e, pp. 397-398 and the Wikipedia RC4 article. RC4 employs an 8x8 substitution box (S-box). The S-box is initialized so that S[i] = i, for i=(0,255). A permutation of the S-box is then performed as a function of the key. The K array is a 256-byte structure that holds the key (possibly supplemented by an Initialization Vector), repeating itself as necessary so as to be 256 bytes in length (obviously, a longer key results in less repetition). [[NOTE: All arithmetic below is assumed to be on a per-byte basis and so is implied to be modulo 256.]] j = 0 Encryption and decryption are performed by XORing a byte of plaintext/ciphertext with a random byte from the S-box in order to produce the ciphertext/plaintext, as follows: Initialize i and j to zero For each byte of plaintext (or ciphertext): i = i + 1 Decryption: plaintext [i] = S[z] ⊕ ciphertext [i] A Perl implementation of RC4 (fine for academic, but not production, purposes) can be found at http://www.garykessler.net/software/index.html#RC4. This program is an implementation of the CipherSaber version of RC4, which employs an initialization vector (IV). The CipherSaber IV is a 10-byte sequence of random numbers between the value of 0-255. The IV is placed in the first 10-bytes of the encrypted file and is appended to the user-supplied key (which, in turn, can only be up to 246 bytes in length). In 2014, Rivest and Schuldt developed a redesign of RC4 called Spritz. The main operation of Spritz is similar to the main operation of RC4, except that a new variable, w, is added: i = i + w Decryption: plaintext [i] = S[z] ⊕ ciphertext
[i] As seen above, RC4 has two pointers into the S-box, namely, i and j; Spritz adds a third pointer, k. Pointer i move slowly through the S-box; note that it is incremented by 1 in RC4 and by a constant, w, in Spritz. Spritz allows w to take on any odd value, ensuring that it is always relatively prime to 256. (In essence, RC4 sets w to a value of 1.) The other pointer(s) — j in RC4 or j and k in Spritz — move pseudorandomly through the S-box. Both ciphers have a single swap of entries in the S-box. Both also produce an output byte, z, as a function of the other parameters. Spritz, additionally, includes the previous value of z as part of the calculation of the new value of z. 5.14. Challenge-Handshake Authentication Protocol (CHAP)CHAP, originally described in RFC 1994, and its variants (e.g., Microsoft's MS-CHAP) are authentication schemes that allow two parties to demonstrate knowledge of a shared secret without actually divulging that shared secret to a third party who might be eavesdropping.
FIGURE 30: CHAP Handshake. The operation of CHAP is relatively straight-forward (Figure 30). Assume that the Client is logging on to a remote Server across the Internet. The Client needs to prove to the Server that it knows the password but doesn't want to reveal the password in any form that an eavesdropper can decrypt. In CHAP:
Since the password is never revealed to a third-party, why can't we then just keep the same password forever? Note that CHAP is potentially vulnerable to a known plaintext attack; the challenge is plaintext and the response is encrypted using the password and a known CHAP algorithm. If an eavesdropper has enough challenge/response pairs, they might well be able to determine the password. Some other issues related to this form of authentication can be found in "Off-Path Hacking: The Illusion of Challenge-Response Authentication" (Gilad, Y., Herzberg, A., & Shulman, H., September-October 2014, IEEE Security & Privacy, 12(5), 68-77). 5.15. Secure E-mail and S/MIMEElectronic mail and messaging are the primary applications for which people use the Internet. Obviously, we want our e-mail to be secure; but, what exactly does that mean? And, how do we accomplish this task? There are a variety of ways to implement or access secure e-mail and cryptography is an essential component to the security of electronic mail. And, the good news is that we have already described all of the essential elements in the sections above. From a practical perspective, secure e-mail means that once a sender sends an e-mail message, it can only be read by the intended recipient(s). That can only be accomplished if the encryption is end-to-end; i.e., the message must be encrypted before leaving the sender's computer and cannot be decrypted until it arrives at the recipient's system. But in addition to privacy, we also need the e-mail system to provide authentication, non-repudiation, and message integrity — all functions that are provided by a combination of hash functions, secret key crypto, and public key crypto. Secure e-mail services or software, then, usually provide two functions, namely, message signing and message encryption. Encryption, obviously, provides the secrecy; signing provides the rest. Figure 4, above, shows how the three different types of crypto schemes work together. For purposes of e-mail, however, it is useful to independently examine the functions of signing and encryption, if for no other reason than while secure e-mail applications and services can certainly sign and encrypt a message, they may also have the ability to sign a message without encrypting it or encrypt a message without signing it. E-mail messages are signed for the purpose of authenticating the sender, providing a mechanism so that the sender cannot later disavow the message (i.e., non-repudiation), and proving message integrity — unless, of course, the sender claims that their key has been stolen. The steps of signing and verifying e-mail are shown in Figure 31. To sign a message:
Verification of the signed message requires the receiver's software to perform the opposite steps as the sender's software. In short, the receiver extracts the sender's Digital Signature, calculates a digital signature based upon the sender's information (e.g., using the sender's public key), and compares the computed signature with the received signature; if they match, the message's signature is verified. Note that if there are multiple recipients of the message, each will perform the same steps to verify the signature because the verification is based upon the sender's information (compare this to decryption, described below). E-mail messages are encrypted for the purpose of privacy, secrecy, confidentiality — whatever term you wish to use to indicate that the message is supposed to be a secret between sender and receiver. The steps of encrypting and decrypting e-mail are shown in Figure 32. To encrypt a message:
Note that if the message has multiple recipients, the encryption step will yield different results because the encryption step is dependent upon the recipient's information (e.g., their public key). One application might choose to send a different encrypted message to each recipient; another might send the same encrypted message to each recipient, but encrypt the decryption key differently for each recipient (note further that this latter approach might allow a recipient to perform a known plaintext attack against the other recipients; each recipient knows the decryption key for the message and also sees the key encrypted with the recipient's information). In any case, recipient-specific information (e.g., their private key) must be used in order to decrypt the message and the decryption steps performed by the recipient are essentially the opposite of those performed by the sender. This discussion, so far, has been a little vague because different applications will act is different ways but, indeed, are performing very similar generic steps. There are two primary ways for a user to get send and receive secure e-mail, namely, to employ some sort of Web-based e-mail service or employ a secure e-mail client.
FIGURE 33: E-mail message to non-4SecureMail user. If the reader is interested in using a Web-based secure e-mail service, you have only to do an Internet search to find many such services. All have slightly different twists to them, but here are a few representative free and commercial options:
The alternative to using a Web-based solution is to employ a secure e-mail client or, at least, a client that supports secure e-mail. Using host-based client software ensures end-to-end security — as long as the mechanisms are used correctly. There are no lack of clients that support secure mechanisms; Apple Mail, Microsoft Outlook, and Mozilla Thunderbird, for example, all have native support for S/MIME and have plug-ins that support OpenPGP/GPG (see Section 5.5 for additional information on the signing and encryption capabilities of PGP). The Secure Multipurpose Internet Mail Extensions (S/MIME) protocol is an IETF standard for use of public key-based encryption and signing of e-mail. S/MIME is actually a series of extensions to the MIME protocol, adding digital signature and encryption capability to MIME messages (which, in this context, refers to e-mail messages and attachments). S/MIME is based upon the original IETF MIME specifications and RSA's PKCS #7 secure message format, although it is now an IETF specification defined primarily in four RFCs:
A quite good overview of the protocol can be found in a Microsoft TechNet article titled "Understanding S/MIME." Content-Type: multipart/signed; boundary="Apple-Mail=_6293E5DF-2993-4264-A32B-01DD43AB4259"; protocol="application/pkcs7-signature"; micalg=sha1 --Apple-Mail=_6293E5DF-2993-4264-A32B-01DD43AB4259 Content-Transfer-Encoding: 7bit Content-Type: text/plain; charset=us-ascii Hi Carol. What was that pithy Groucho Marx quote? /kess --Apple-Mail=_6293E5DF-2993-4264-A32B-01DD43AB4259 Content-Disposition: attachment; filename=smime.p7s Content-Type: application/pkcs7-signature; name=smime.p7s Content-Transfer-Encoding: base64 MIAGCSqGSIb3DQEHAqCAMIACAQExCzAJBgUrDgMCGgUAMIAGCSqGSIb3DQEHAQAAoIIJ9TCCBK8w ggOXoAMCAQICEQDgI8sVEoNTia1hbnpUZ2shMA0GCSqGSIb3DQEBCwUAMG8xCzAJBgNVBAYTAlNF MRQwEgYDVQQKEwtBZGRUcnVzdCBBQjEmMCQGA1UECxMdQWRkVHJ1c3QgRXh0ZXJuYWwgVFRQIE5l dHdvcmsxIjAgBgNVBAMTGUFkZFRydXN0IEV4dGVybmFsIENBIFJvb3QwHhcNMTQxMjIyMDAwMDAw WhcNMjAwNTMwMTA0ODM4WjCBmzELMAkGA1UEBhMCR0IxGzAZBgNVBAgTEkdyZWF0ZXIgTWFuY2hl c3RlcjEQMA4GA1UEBxMHU2FsZm9yZDEaMBgGA1UEChMRQ09NT0RPIENBIExpbWl0ZWQxQTA/BgNV BAMTOENPTU9ETyBTSEEtMjU2IENsaWVudCBBdXRoZW50aWNhdGlvbiBhbmQgU2VjdXJlIEVtYWls IENBMIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAibEN2npTGU5wUh28VqYGJre4SeCW 51Gr8fBaE0kVo7SMG2C8elFCp3mMpCLfF2FOkdV2IwoU00oCf7YdCYBupQQ92bq7Fv6hh6kuQ1JD 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Figure 34 shows a sample signed message using S/MIME. The first few lines indicate that this is a multipart signed message using the PKCS #7 signature protocol and, in this case, the SHA-1 hash. The two text lines following the first --Apple-Mail=... indicates that the message is in plaintext; this is followed by the actual message. The next block indicates use of S/MIME where the signature block is in an attached file (the .p7s extension indicates that this is a signed-only message), encoded using BASE64. Content-Type: application/pkcs7-mime; name=smime.p7m; smime-type=enveloped-data Content-Transfer-Encoding: base64 MIAGCSqGSIb3DQEHA6CAMIACAQAxggHOMIIBygIBADCBsTCBmzELMAkGA1UEBhMCR0IxGzAZBgNV BAgTEkdyZWF0ZXIgTWFuY2hlc3RlcjEQMA4GA1UEBxMHU2FsZm9yZDEaMBgGA1UEChMRQ09NT0RP IENBIExpbWl0ZWQxQTA/BgNVBAMTOENPTU9ETyBTSEEtMjU2IENsaWVudCBBdXRoZW50aWNhdGlv biBhbmQgU2VjdXJlIEVtYWlsIENBAhEA70Uu5F7X63+/i82e2a7zmzANBgkqhkiG9w0BAQEFAASC AQAbKAO7BoEKgZ9e/C837YpZYzspGdLbiMnRPmz3p2v+8H9DgPcOzMAjwdvT94el3hguke/Dn4LK L4/Un9ZbruoPzfps0Cxa8A+Acw2fVluYImKs0y3zCCOCQiKwW4IMWmS0HCvFTrHKGuGcWmpaFUv1 vTdFNPhQzF6jRJPv35GNtHWEFIRwqWFG1jOh/0uX0o3Cg8B1j/wwjTEkd0WU/DzYbe6nQSJzh7Kz 9guBAyfSVPZsLcvkd1ftP4vVrILnafKaFK9ls3al8dT5+oY7oTUHhem+oPMLcOnX0+ZZcqs97+oW HvQQy1lpofU8b/0Qt8lYZfAC5lMIOg6nMbmIUdjOMIAGCSqGSIb3DQEHATAUBggqhkiG9w0DBwQI hd7YXnfGNOeggAQYdIYlsYppSpTleDWPMbopt2Zu7+umGjuHBAiuLupldkuMbwQYorVXhHJ3J6G3 0Rad+eC3vbpu4Ohtcz/rBBAhZ97y8YgLhmSJzXCSLh5UBAisFO1grQ/WgQQIpwnzeRUrRikEMMo/ qTMXMBaFFmGRHgSbVaNTJOcpk11kmrZbUWUdSWUZwQ3TSdvnyVUJUUf7gFs8eQQop2w/yLoGZGVY DJFpaCBEbgBZAXbWeducGiDR8lUYOPdwjSnfb96yBgQIN2WZZMiZ6x4ECMQJ5uftbc+dBAj/LNyO TGk4awAAAAAAAAAAAAA= FIGURE 35: Sample S/MIME encrypted message. Figure 35 shows a sample encrypted message, carried as an S/MIME enveloped data attachment (.p7m) file, also formatted in BASE64. S/MIME can also attach certificate management messages (.p7c) and compressed data (.p7z). Many more S/MIME sample messages can be found in RFC 4134 ("Examples of S/MIME Messages").
FIGURE 36: Sample S/MIME certificate. S/MIME is a powerful mechanism and is widely supported by many e-mail clients. To use your e-mail client's S/MIME functionality, you will need to have an S/MIME certificate (Figure 36). Several sites provide free S/MIME certificates for personal use, such as Instant SSL (Comodo), Secorio, and StartSSL (StartCom); commercial-grade S/MIME certificates are available from many other CAs. (NOTE: If these sites install your S/MIME certificate to your browser, you might need to export [backup] the certificate and import it so it can be seen by your e-mail application.) Do note that S/MIME is not necessarily well-suited for use with Web-based e-mail services. First off, S/MIME is designed for true end-to-end (i.e., client-to-client) encryption and Web mail services provide server-to-server or server-to-client encryption. Second, while S/MIME functionality could be built into browsers, the end-to-end security offered by S/MIME requires that the private key be accessible only to the end-user and not to the Web server. Finally, end-to-end encryption makes it impossible for a third-party to scan e-mail for viruses and other malware, thus obviating one of the advantages of using a Web-based e-mail service in the first place. 5.16. Identity-Based Encryption (IBE)Identity-Based Encryption is a public-key crypto scheme that can be used for key authentication by parties who do not have an a priori relationship. First proposed in 1984 by Adi Shamir, a sender can encrypt a message using the receiver's public key, which can be derived from an ASCII character string that represents some unique identifier of the receiver (e.g., an e-mail address, telephone number, or a ship's registry number). IBE employs most of the concepts that we already know from other PKC schemes. First, every user has a private/public key pair, where the public key is widely distributed and the private key is a closely held secret. Second, while the keys in the key pair are mathematically related, a party that knows someone's public key cannot easily derive the matching private key. Finally, key distribution and management requires a trusted third-party — called the Private Key Generator (PKG) — but, unlike the certificate authority (CA) model, does not require an a priori relationship between the users and the PKG. In an IBE system, the PKG generates its own master public/private key pair. The PKG can publish and distribute the Master Public Key, along with the algorithm used to derive keys; the PKG closely holds the Master Private Key as a secret. Any user in the IBE system can generate a public key using a unique identifying string (ID) in combination with the Master Public Key and the key-generation algorithm. In order to obtain a private key, the owner of the identifying string contacts the PKG which, in turn, derives the appropriate private key from the ID in combination with the Master Private Key. By way of example, consider the case where Alice wants to send an encrypted message to Bob. Bob's email address, , is his unique ID string. Using the PKG's Master Public Key, Alice can derive Bob's public key from his ID string. With that, she can encrypt a message for Bob and send it to him. When Bob receives the message, he contacts the PKG and, using some mechanism specified by the PKG, authenticates himself as the true owner of the ID string. The PKG can then use Bob's ID string and the Master Private Key to derive his private key, which is then sent to Bob. At that point, Bob can decrypt Alice's message. Once Bob has his private key, of course, he can continue to use it for subsequent messages. Using a similar but reverse process, Alice could use her own unique ID string (e.g., ) to obtain her private key from the PKG with which she could digitally sign the e-mail message that she sends to Bob. Bob would then use Alice's ID string to derive her public key in order to verify the signature. In 2001, Dan Boneh from Stanford University and Matt Franklin from the University of California, Davis developed a practical implementation of IBE based on elliptic curves and a mathematical construct called the Weil Pairing. Clifford Cocks, from the U.K.'s Government Communications Headquarters (GCHQ), described another IBE solution based on quadratic residues in composite groups, also in 2001.
FIGURE 37: Identity-based encryption schema. Boneh and Franklin defined four basic functions that an IBE system needs to employ (Figure 37):
The most practical IBE algorithms are based on elliptical curves, and include Boneh-Franklin (BF-IBE), Sakai-Kasahara (SK-IBE), and Boneh-Boyen (BB-IBE). Cocks' solution causes so much overhead (i.e., ciphertext expansion) as to be impractical expect for very short messages, such as key exchange for a secret key crypto scheme. (This is, ironically, where PKC schemes find themselves, in general; in the 1970s, PKC took up to three orders of magnitude more compute time than an SKC scheme to encrypt a message, thus the use of PKC for key exchange.) RFC 5091: Identity-Based Cryptography Standard (IBCS) #1 describes an implementation of IBE using Boneh-Franklin (BF) and Boneh-Boyen (BB1) Identity-based Encryption. IBE has its pros and cons but is particularly useful in very dynamic environments where pre-distribution of public keys is not possible or not feasible. It requires, of course, that the PKG is highly trusted. The PKG is also a lucrative target for hackers because compromise of the PKG compromises every message sent by parties employing the system. 5.17. Shamir's Secret Sharing (SSS)Shamir's Secret Sharing is a rather novel secret-sharing method where a group can work together to gain access to a resource. Adi Shamir, of RSA fame, described a method whereby a secret is divided into n parts in such a way that knowledge of any k parts allows the secret to be revealed; knowledge of any k-1 or fewer parts yields no information about the secret at all. This so-called (k,n) threshold scheme has many applications in real life. Consider this simple example from Shamir's original 1979 paper, "How to Share a Secret":
The idea is conceptually straight-forward. Observe that a polynomial of degree k-1 is defined by k terms; e.g., the 2nd-degree polynomial 4x2+6x+15 has three terms. Suppose the
secret, S, can be expressed as a number. We choose a prime number, P, so that S f(x) = a0 + a1x + a2x2 + ... + ak-1xk-1 where a0=S and the remaining
coefficients are random positive integers such that ai We can now build a table of n values of the polynomial; i.e., f(i) for i = 1...n. At this point, each of the n participants in the (k,n) scheme is given a different value of i in the range 1-n, as well as the corresponding integer output, f(i). If any subset of k participants puts
their information together, they can reconstruct a polynomial of degree k-1 so that the a0 term takes on the value of the original secret, S. This is based on the fact that the system is designed so that the secret, divided into parts, can be estimated — or interpolated — by knowledge of any k of the parts. So, here is a simple, but reasonably accurate, example of how SSS works. (It is simplified because it will employ integer arithmetic
whereas the SSS scheme actually employs finite field arithmetic, resulting in a less than totally secure system; nevertheless, the reader should get the idea.) Let's build a (3,5) threshold system; i.e., one where the secret is split across five pieces and any three are required to reconstruct the secret. In this case, the secret, S, is represented by the number 18. We will choose 23 as the prime number P (which is larger than S, as required). Since k=3, we
need to create a polynomial of degree 2. This polynomial will need three coefficients; a0=S, and we will randomly choose a1=6 and a2=11 (as required, all values of a are smaller than P.) We now have the polynomial: f(x) = 18 + 6x + 11x2 The next step is to create the table of the five outputs of the function, f(x), for all values x=1,...,5; each
(x,f(x)) pair is denoted Tx: T1 = (1,35) Each of the five participants is provided with one of the T pairs. Now, let's see what happens when participants 1, 3, and 4, for example, get together to reconstruct the secret. The SSS scheme relies on the fact that k points
can be used to estimate the original n-part problem. For the reconstruction, we need to compute Lagrange polynomials — denoted L — which are used for polynomial interpolation. The Lagrange method finds the lowest degree polynomial that represents a function that coincides at a set of given points. In this example, we have three points: (x0,y0)=T1=(1,35),
(x1,y1)=T3=(3,135), and (x2,y2)=T4=(4,218). The formulas and solutions for the three Lagrange polynomials are: The next step is to solve the Lagrange problem: It turns out that the only coefficient that matters is the one for the x0 (ones) term, which is 18. This, of course, is the a0 coefficient which, by design, is the secret, S. This also points to a computational shortcut, namely, we can ignore any calculation involving any part of the polynomial other than the x0 term. Now, the calculation is merely: f(x) = (35 ⋅ 2) + (135 ⋅ -2) + (218 ⋅ 1) = 18 = S
Shamir's original paper describes this pretty well and the Wikipedia page has a very detailed example. Hash functions are used in crypto systems for message integrity, so that Bob can be ensured that the message he receives is the one that Alice sent. Hash functions do this by detecting bit errors in messages; even a single bit error in a large
message will cause a significant change in the hash value. Hash functions, however, were not originally designed for message integrity; back in the early days of computer communications, longitudinal redundancy check (LRC) and cyclic redundancy check (CRC) algorithms, including the use of parity bits, were employed for bit error detection. An LRC code is pretty trivial and operates on the bytes of the message. Generally, an LRC might merely take the exclusive-OR of all of the bytes in the
message or compute the sum of all of the bytes, and append the checksum value to end of the message. While there are many variants of this, here are two examples. Suppose my message is the character string: My name is Gary. Using the ASCII character code, this message would appear in hexadecimal as 4D79206E616D6520697320476172792E. Taking the XOR of each byte would yield an LRC of 0x0A; summing the individual bytes (modulo 256) would yield a sum of 0x9C.
When transmitting the message, the LRC bytes are appended to the end of the message. The receiver also calculates the LRC on the message and the receiver's value should match the transmitted value. LRCs are very weak error detection mechanisms. If there is a single bit error, it will certainly be detected by an LRC. But an even number of errors in the same bit position within multiple bytes will escape detection by an XOR LRC. And a burst of errors might even escape detection by an
additive LRC. The point is, it is trivial to create syndromes of bit errors that won't be found by an LRC code. (This is not to say that they are not used in some data transmission systems!) CRCs were developed in the early 1960s to provide message integrity, bit-error detection, and, in some cases, bit-error correction in data communication systems. There are many CRC codes in use today, almost all in some sort of networking application. CRCs are expressed as an n-order polynomial
yielding an n-bit result; i.e., a CRC-n polynomial is one with n+1 terms and is used to compute an n-bit checksum. An n-bit CRC code can be used with an arbitrary length input, can detect 100% of burst errors up to n bits in length, and can detect bursts of n bits or more with probability (1-2-n). Common CRCs today yield checksums of 8, 16, 32, or 64 bits in length although other lengths are also used in some applications. Two example 16-bit CRCs are: If we take our message above, for example, the CRC-CCITT checksum value would be 0xBF9D. FIGURE 38: Hardware CRC-16-CCITT generator. (From Microchip
AN730)
CRCs are, in essence, a one-way stream cipher, receiving one bit of the message at a time, and using XOR gates and an n-bit shift register to compute the checksum. The contents of the register are the checksum value, where the register is generally initialized as all zeroes or all ones. This operation can be seen by looking at the hardware implementation of the CRC-16-CCITT checksum (Figure 38), taken from
Microchip Application Note 730 (AN730). Now, this stroll down memory lane (at least for me!) is really about why LRCs and CRCs are not used in cryptography. While they work fine for bit error detection and the fact that an arbitrary-length input produces a fixed-length output, they were not designed for the level of robustness required for cryptographic error detection and other functions.
The origins of cryptographic hash functions (CHFs) date back to the early 1950s, when hash functions — aka, message digests — were used in computer science to map an arbitrary length data item to a bit array of fixed size; e.g., one application was to map variable-length variable names to a fixed-size token array for processing variables in a programming language's compiler or interpreter. It took another 20 years for hashing to be applied to cryptography. Like a CRC, a CHF algorithm
incorporated into a modern cryptosystem (say, starting in the late-1980s or early-1990s) can, theoretically, accept a message of arbitrary length and produce a fixed-length output. And, like CRCs, it is believed that it is computationally infeasible to produce two messages having the same message digest value or to produce a message having a given prespecified message digest value, given a strong message digest algorithm. Unlike CRCs, message digest algorithms are intended for digital
signature applications; signing the "compressed" version of a message (i.e., the hash) is far more efficient than signing the entire message. Furthermore, signing the hash value takes the same amount of time regardless of the size of the message, thus making the time required for signing to be much more predictable than if signing an arbitrary length message. Also unlike CRCs, message digest algorithms have an encryption function integral to their computation. Among the earliest hash
algorithm incorporated into cryptosystems was Message Digest 5, described in 1992 in RFC 1321; the Secure Hash Algorithm came later, described in 2001 in RFC 3174. MD5 and SHA-1 produce a 128-bit and 160-bit output, respectively; MD5 accepts a message of arbitrary length while SHA-1 limits the input to 264-1 bits. The string above would generate
the following hash values: MD5 ("My name is Gary.") = 3b55c9c3503c456906b765fbaaf37223 While hash algorithms are designed to be as simple as possible, they are much more complex than a CRC. So, here's a rundown on part of the MD5 calculation to give an idea of the manipulations. See the RFCs for sample code. First off, MD5 operates on 128-bit blocks or, more precisely, four 32-bit words, at one time.
Therefore, the initial step is to pad the incoming message so that it is an even multiple of 16 32-bit words (512 bits). The algorithm then steps through the input 128 bits at a time. I'll explain the process below and you'll see multiple passes over the data with a lot of transpositions and substitutions, which are the basic operations of encryption that were described earlier in this paper. So, here is some basic MD5 terminology and nomenclature: The MD5 algorithm processes one 128-bit block as a time, sequentially stepping through the message. There is a feedback mechanism in place because all computations use the A, B, C, and D registers without zeroing them out between blocks. There are four rounds of processing on each 128-bit block, and each round comprises 16 operations. Each of the 64 operations uses the following
generic formula: a = b + ((a + f(b,c,d) + X[k] + T[i]) <<< s) where: The table below summarizes the characteristics of each operation within each round; remember that we start with operations 1-16 in round 1, then move on to round 2, etc.: The way to interpret the information in the table is as follows. Remember, the generic formula for all operations is: a = b + ((a + f(b,c,d) + X[k] + T[i]) <<< s) So, if you want to understand, say, operation 11 in Round 3, the table says: Given these
values, the operation for this round would be computed as: C = D + ((C + H(D,A,B) + X[3] + T[43]) <<< 16) IPsec authentication (for both AH and ESP), the Signal protocol, and many other communication schemes use HMAC, a Keyed-Hashing Message Authentication Code, to allow two users to mutually authenticate by demonstrating that they both know a secret without actually explicitly exchanging that
secret. Described in FIPS PUB 198 and RFC 2104, HMAC uses a shared secret key between two parties rather than public key methods for message authentication. The advantage of this method of authentication is a simplicity in processing; PKC algorithms generally require three to five orders of magnitude (i.e., 1,000-100,000 times) more
processing than an SKC scheme operating over the same message. If an application requires nothing more than authentication and needs fast processing, HMACs are an attractive alternative. The generic HMAC procedure can be used with just about any hash algorithm. In HMAC, both parties share a secret key. The secret key will be employed with the hash algorithm in a way that provides mutual authentication without transmitting the key on the communications channel. Some key management
procedure, external to the HMAC protocol, is used to manage key exchange between the two parties. Recall that hash functions operate on fixed-size blocks of input at one time; MD5 and SHA-1, for example, work on 64-byte blocks. These functions then generate a fixed-size hash value; MD5 and SHA-1 produce 16-byte (128-bit) and 20-byte (160-bit) output strings, respectively. For use with HMAC, the secret key (K) should be at least as long as the hash output.
FIGURE 39: Keyed-hash MAC operation. The following steps provide a simplified, although reasonably accurate, description of how the HMAC scheme would work with a particular plaintext MESSAGE (Figure 39): HMACs are ideal for communication between two parties, say, Alice and Bob, who have a shared secret. They
don't work as well in any sort of multicast environment, because all of the receivers — and there could be millions — would all have a single shared secret key. In a zero-trust environment, this greatly raises the opportunity for a rogue group member to send bogus messages. The common solution to this problem, of course, is to use a PKC methodology and employ a digital signature; Alice, for example, creates a signature with her private key and Bob, Carol, Dave, and all the other receivers can
verify the signature using Alice's public key. In this case, none of the receivers who hold Alice's public key can spoof being Alice because they can't generate her signature. Indeed, the digital signature also provides the property of non-repudiation. The problem with digital signatures is that they require a lot of computation for both sender and receiver(s); remember, PKC can require at least 1,000 times more processing for a given message compared to an SKC scheme. The resultant
signature also reduces the bandwidth efficiency on a communications channel. So, digitally signing messages in a broadcast or large multicast environment where receivers want to authenticate each transmission is a challenge. (See the next section on TESLA for one possible solution.) The Timed Efficient Stream Loss-tolerant Authentication (TESLA) protocol, described in
RFC 4082, provides a bandwidth-efficient, fault-tolerant mechanism so that a single key can be used for authentication by a large number of receivers in a multicast/broadcast environment. TESLA uses an HMAC-type scheme to provide time-delayed message authentication. The basic idea is that the sender uses a key for only a certain time interval (e.g., one second); during that time interval, receivers buffer all of the incoming
messages. During the next time interval, the sender shares the previous interval's key with the receivers and starts to use a new key; receivers can now authenticate the buffered messages from the prior time interval even as they buffer new incoming messages. TESLA requires the sender to generate a chain of authentication keys, where a given key is associated with a single time slot, T. In general, Ti+1 = Ti+Δt. The sender can create as many keys as it
wants but might need to limit the length of the chain based upon memory or other constraints. So, suppose the sender wants to create a chain of N keys. The sender will randomly select the N-th key, KN. Then, using a pseudo-random number generator (PRNG) function, P, and the prior key value as the seed, the sender creates the next key in the chain. Thus, KN-1 = P(KN), KN-2 = P(KN-1),...,
K0 = P(K1). Each key is assigned to a time interval, so that Ki is associated with Ti. One important feature is that this is a one-way chain; given any key, Ki, all previously used keys can be derived by the receiver (i.e., any Kj can be calculated where j The operation of TESLA is relatively straight-forward.
During the T0 time slot, the sender employs an HMAC where K0 is the secret key. These messages are buffered by one or more receivers. When the T1 time slot starts, the sender sends K0 to the receiver(s) and starts to use K1 as the secret key. The receiver(s) can now authenticate the T0 buffered messages. Because of the properties of the one-way chain, the receiver(s) can derive keys from previous time slots that might have been
lost due to transmission errors, thus providing fault tolerance. For obvious reasons, TESLA requires loosely synchronized clocks between the sender and the receivers, but is not really intended for real-time services that cannot tolerate any delay. Check out the RFC or the paper by Perrig, Canetti, Tygar, and Song in RSA CryptoBytes for more detail. A light-weight version
of the protocol, called µTESLA, was designed for sensor networks that have limited processing power, limited memory, and a real-time communication requirement. This version provides nearly immediate distribution of the authentication key and RC5 encryption. µTESLA is described in a paper by Perrig, Szewczyk, Tygar, Wen, and Culler in the ACM Journal of Wireless Networks. When this paper was originally prepared, most crypto schemes were designed using basic integer arithmetic, logarithms and exponents, and prime number factorization, all for what today can only be described as classic computers. Resistance to brute-force attacks was provided by the expediency of using very large keys and requiring periodic changes to the key in order to "outlast" the available
computing power necessary to try and guess every possible key value within the keyspace. Quantum computers, quantum algorithms, and quantum cryptography are changing the paradigms of modern and future cryptography. I am not an expert in this area so I am not going to talk about this subject in any great detail, but here is a quick intro and some pointers to additional information. Today's computers employ a von Neumann architecture, based upon the design model introduced by Johnny
von Neumann in the 1940s. Quantum computing requires an entirely new way of looking at computer hardware. The basic difference between a classic computer and a quantum computer is the concept of a bit. In classic computers, a bit — aka binary digit — can take on only two values, namely, 0 or 1. A combination of two bits can take on four values — 00, 01, 10, and 11. To generalize, an n-bit string can take on 2n values, 0-(2n-1). While classic computers
define bits based upon storing data as electrical signals, quantum computers define storage based upon electrons and photons that can encode the data in multiple states. A quantum bit, or qubit, can take on a state that is some combination of both 0 and 1 simultaneously. This is due to a phenomenon known as superposition. This means that two qubits can take on the four values mentioned above — 00, 01, 10, and 11 — at the same time! FIGURE 40: Classical computing bit and quantum computing qubit. (Strathclyde University) There are many sources of information about quantum computing online and in various journal papers and articles. Here are a few places
where you can start: In theory, a quantum computer can solve problems that are too computationally complex for a today's conventional computers. The implications for using quantum methods to attack classic cryptography algorithms should be readily apparent. Since we can theoretically build a computer where an n-qubit device can take on 2n states at the same time, it renders an n-bit keyspace
susceptible to a nearly immediate brute force attack. Before any panic sets in, recognize that quantum computers today are relatively small, so a large key (say, 256 bits or larger) is as safe today from a quantum computer brute force attack as a smaller key (e.g., 128 bits or smaller) is against an attack from a classic computer. Clearly, there will be this battle for some time keeping the keys large enough to withstand quantum attacks. (This is similar to the increasing size of RSA keys to
keep them computationally infeasible to factor.) Meanwhile, a functional quantum computer that can pose a serious attack of cryptography schemes as we know them today does not exist, and won't for many years — if ever. Meanwhile, it would be folly to ignore the potential threat and be blindsided. In any case, many PKC schemes are at greater risk than SKC schemes. Most PKC schemes — including RSA — use some form of prime factorization. Even though PKC schemes typically use keys that are an
order of magnitude larger than SKC methods, the prime factorization algorithms are susceptible to Shor's algorithm, a quantum computer method for finding the prime factors of an integer. The classic method to determine the prime factors of an integer is called the general number field sieve. The time required to factor an integer, N, with the field sieve algorithm rises exponentially, increasing as a function of elog N. Shor's algorithm, developed by Peter Shor in
1994, can solve the problem in polynomial time, or a value that is a function of log N. NOTE: Here's a quick word on e and log. Euler's Number — known as e — is an irrational number with a value 2.7182818284590452353.... It is the basis for natural logarithms (ln) and many other applications in mathematics. When we say that some set of values increase exponentially, we mean as a power of e. A base 10 logarithm, or log, of a number is
the power of 10 that equals the number so, for example, log 100 = 2 because 102=100. The table below shows some example values. Powers of e grow quite rapidly while logarithms increase slowly and this clearly impacts computational complexity. Problems that grow exponentially in terms of complexity eventually rise to a level such that, while the algorithm is known, no computer can actually provide a solution. Quantum computers can reduce the complexity of some of these problems so that they become computationally feasible. In terms of cryptography, if a quantum computer
with a sufficient number of qubits could operate without succumbing to some of the problems of quantum computing (e.g., quantum noise and other quantum-decoherence phenomena), then Shor's algorithm could be used to break such PKC schemes as RSA, Diffie-Hellman key exchange, and Elliptic Curve Diffie-Hellman key exchange. It won't affect SKC schemes such as AES because it is not based on prime factorization. Again, there's a ton more that you can read about this topic; here are some
starting points: The paragraphs above are preamble to an introduction to NIST's post-quantum cryptographic standard (PQCS). In 2016, NIST started a competition to replace current PKC and digital signature algorithms with quantum-resistant cryptography, new methods that include "cryptographic algorithms or
methods that are assessed not to be specifically vulnerable to attack by either a CRQC [cryptanalytically relevant quantum computer] or classical computer" (Prepare for a New Cryptographic Standard to Protect Against Future Quantum-Based Threats, July 5, 2022). NIST has successfully used open competitions in the past, resulting in a
new SKC standard (AES) in 2001 and new hash function standard (SHA-3) in 2015. NIST received 82 proposals from around the world in 2017; 69 submissions made it through the Round 1 review, although five were subsequently withdrawn. In 2019, 26 submissions, including 17 Public-key Encryption and Key-establishment Algorithms, and 9 Digital Signature Algorithms, were announced as Round 2 finalists. Seven of the algorithms, including four Public-key Encryption and Key-establishment Algorithms, and
three Digital Signature Algorithms (plus eight alternate candidates) became Round 3 finalists in 2020. Finally, four Public-key Encryption and Key-establishment Algorithms — BIKE, Classic McEliece, HQC, and SIKE — became Round 4 finalists in July 2022. Although the competition has been going on for several years, new cryptanalytic methods have been discovered that can be used against classic and post-quantum algorithms, and new weaknesses are being found in late-round algorithms. So, the process
continues and the future will be one of determining the viability of building quantum computers and the ability to build quantum cryptographic algorithms. As usual, a massive amount of information can be found in the Web. Again, here are some places to start looking: This paper has briefly (well, it started out as "briefly"!) described how digital cryptography works. The reader must beware, however, that there are a
number of ways to attack every one of these systems; cryptanalysis and attacks on cryptosystems, however, are well beyond the scope of this paper. In the words of Sherlock Holmes (ok, Arthur Conan Doyle, really), "What one man can invent, another can discover" ("The Adventure of the Dancing Men," in: The Return of Sherlock Holmes, 1903). There are a lot of topics that have been discussed above that will be big issues going forward in cryptography. As compute power increases,
attackers can go after bigger keys and local devices can process more complex algorithms. Some of these issues include the size of public keys, the ability to forge public key certificates, which hash function(s) to use, and the trust that we will have in random number generators. Interested readers should check out "Recent Parables in Cryptography" (Orman, H., January/February 2014, IEEE Internet Computing, 18(1), 82-86). Cryptography is a particularly interesting field
because of the amount of work that is, by necessity, done in secret. The irony is that secrecy is not the key (no pun intended) to the goodness of a cryptographic algorithm. Regardless of the mathematical theory behind an algorithm, the best algorithms are those that are well-known and well-documented because they are also well-tested and well-studied! In fact, time is the only true test of good cryptography; any cryptographic scheme that stays in use year after year is most likely
a good one. The strength of cryptography lies in the choice (and management) of the keys; longer keys will resist attack better than shorter keys. The corollary to this is that consumers should run, not walk, away from any product that uses a proprietary cryptography scheme, ostensibly because the algorithm's secrecy is an advantage. The observation that a cryptosystem should be secure even if everything about the
system — except the key — is known by your adversary has been a fundamental tenet of cryptography for well over 125 years. It was first stated by Dutch linguist Auguste Kerckhoffs von Nieuwenhoff in his 1883 (yes, 1883) papers titled La Cryptographie militaire, and has therefore become known as "Kerckhoffs' Principle." SIDEBAR: Getting a new crypto scheme accepted, marketed, and, commercially viable is a hard problem particularly if someone wants to make money off of the invention of a "new, unbreakable" methodology. Many people want to sell their new algorithm and, therefore, don't want to expose the scheme to the public for fear that their idea will be stolen. I observe that, consistent with Kerckhoffs' Principle, this approach is doomed to fail. A company won't invest in a secret
scheme because there's no need; one has to demonstrate that their algorithm is better and stronger than what is currently available before someone else will invest time and money to explore an unknown promise. Regardless, I would also suggest that the way to make money in crypto is in the packaging — how does the algorithm fit into user applications and how easy is it for users to use? Check out a wonderful paper about crypto usability, titled
"Why Johnny Can't Encrypt" (Whitten, A., & Tygar, J.D., 1999, Proceedings of the 8th USENIX Security Symposium, August 23-26, 1999, Washington, D.C., pp. 169-184.). As a slight aside, another way that people try to prove that their new crypto scheme is a good one without revealing the mathematics behind it is to provide a public challenge where the author
encrypts a message and promises to pay a sum of money to the first person — if any — who cracks the message. Ostensibly, if the message is not decoded, then the algorithm must be unbreakable. As an example, back in ~2011, a $10,000 challenge page for a new crypto scheme called DioCipher was posted and scheduled to expire on 1 January 2013 — which it did. That was the last that I heard of DioCipher. I leave it to the reader to consider the validity and usefulness of the public challenge
process. Finally, I can't ignore crypto snake oil or, to be fair, things that appear to be snake oil. The saga of Crown Sterling, a self-proclaimed "leading digital cryptography firm," is a case in point. Crown Sterling revealed a scheme called TIME AI™ — "the World's First 'Non-factor' Based Quantum Encryption Technology" — at BlackHat 2019. Sounds pretty cool but even a shallow analysis shows a lot of use of buzzwords, hand-waving,
and excellent graphics... but no math, no algorithms, and no code. There's been a lot written about this and it is a good case study for the student of cryptography; for a short list, see: And for a purely enjoyable fiction book that combines cryptography and history, check out Neal Stephenson's Cryptonomicon (published May 1999). You will also find in it a new secure crypto scheme based upon an ordinary deck of cards
(ok, you need the jokers...) called the Solitaire Encryption Algorithm, developed by Bruce Schneier. Finally, I am not in the clothing business although I did used to have an impressive t-shirt collection (over 350 and counting, at one point!). I still proudly wear the DES (well, actually the IDEA) encryption algorithm t-shirt from 2600 Magazine which, sadly, appears to be no longer available (left). (It was always ironic to me that The Hacker Quarterly got the algorithm wrong but...) A t-shirt with Adam Back's RSA Perl code can be found at
http://www.cypherspace.org/~adam/uk-shirt.html (right). A number of readers over time have asked for some rudimentary background on a few of the less well-known mathematical functions mentioned in this paper. Although this is purposely not a mathematical treatise, some of the math functions mentioned here are essential to grasping how modern crypto functions work. To that end, some of the mathematical functions
mentioned in this paper are defined in greater detail below. George Boole, a mathematician and philosopher in the mid-1800s, invented a form of algebra with which to express logical arguments. Boolean algebra provides the basis for building electronic computers and microprocessor chips. Boole defined
a bunch of primitive logical operations where there are one or two inputs and a single output depending upon the operation; the input and output are either TRUE or FALSE. The most elemental Boolean operations are: The four Boolean functions are generally represented by the use of a truth tables; in computers, Boolean logic is implemented in logic gates. For design purposes, NOT has one input and the other three functions have two inputs (black); all have a single output (red). The logic diagrams appear below: XOR is one of the fundamental mathematical operations used in cryptography (and many other applications). In an XOR operation, the output will be a 1 if exactly one input is a 1; otherwise, the output is 0. The real significance of this is to look at the "identity properties" of XOR. In particular, any value XORed with itself is 0 (i.e., x ⊕ x = 0) and any value XORed with 0 is just itself (i.e., x ⊕ 0 = x). Why does this matter?
Well, if you take a plaintext string of 0s and 1s, and XOR it with a key string of 0s and 1s, you get a new jumbled string of 0s and 1s. If you then take that jumble and XOR it with the same key, you return to the original plaintext. NOTE: Boolean truth tables usually show the inputs and output as a single bit because they are based on single bit inputs, namely, TRUE and FALSE. In addition, we tend to apply Boolean operations bit-by-bit. For convenience, I have created
Boolean logic tables when operating on bytes. The modulo function is, simply, the remainder function. It is commonly used in programming and is critical to the operation of any mathematical function using digital computers. To calculate X modulo Y (usually written X mod Y), you merely determine the remainder after removing all
multiples of Y from X. Clearly, the value X mod Y will be in the range from 0 to Y-1. Some examples should clear up any remaining confusion: Modulo arithmetic is useful in crypto because it allows us to set the size of an operation and be sure that we will never get numbers that are too large. This is an important consideration when using digital computers. Information theory is the formal study of reliable transmission of information in the least amount of space or, in the vernacular of information theory, the fewest symbols. For purposes of digital communication, a symbol can be a byte (i.e., an eight-bit octet) or an even smaller unit of transmission. The father of information theory is Bell Labs scientist and MIT professor
Claude E. Shannon. His seminal paper, "A Mathematical Theory of Communication" (The Bell System Technical Journal, Vol. 27, pp. 379-423, 623-656, July, October, 1948), defined a field that has laid the mathematical foundation for so many things that we take for granted today, from data compression, data
storage, data communication, and quantum computing to language processing, plagiarism detection and other linguistic analysis, and statistical modeling. Information theory also applies to cryptography, and a student of information theory and cryptography will most certainly want to see the International Association for Cryptologic Research's page on Shannon's 1945 paper, "A Mathematical Theory of Cryptography." There
are many everyday computer and communications applications that have been enabled by the formalization of information theory, such as: One of the key concepts of information theory is that
of entropy. In physics, entropy is a quantification of the disorder in a system; in information theory, entropy describes the uncertainty of a random variable or the randomness of an information symbol. As an example, consider a file that has been compressed using PKZip. The original file and the compressed file have the same information content but the smaller (i.e., compressed) file has more entropy because the content is stored in a smaller space (i.e., with fewer symbols) and each
data unit has more randomness than in the uncompressed version. In fact, a perfect compression algorithm would result in compressed files with the maximum possible entropy; i.e., the files would contain the same number of 0s and 1s, and they would be distributed within the file in a totally unpredictable, random fashion. As another example, consider the entropy of passwords (this text is taken from my paper,
"Passwords — Strengths And Weaknesses," citing an example from Firewalls and Internet Security: Repelling the Wily Hacker by Cheswick & Bellovin [1994]): Most Unix systems limit passwords to eight characters in length, or 64 bits. But Unix only uses the seven significant bits of each character as the encryption key, reducing the key size to 56 bits. But even this is not as good as it
might appear because the 128 possible combinations of seven bits per character are not equally likely; users usually do not use control characters or non-alphanumeric characters in their passwords. In fact, most users only use lowercase letters in their passwords (and some password systems are case-insensitive, in any case). The bottom line is that ordinary English text of 8 letters has an information content of about 2.3 bits per letter, yielding an 18.4-bit key length for an 8-letter passwords
composed of English words. Many people choose names as a password and this yields an even lower information content of about 7.8 bits for the entire 8-letter name. As phrases get longer, each letter only adds about 1.2 to 1.5 bits of information, meaning that a 16-letter password using words from an English phrase only yields a 19- to 24-bit key, not nearly what we might otherwise expect. Encrypted files tend to have a great deal of randomness. This is why a compressed file
can be encrypted but an encrypted file cannot be compressed; compression algorithms rely on redundancy and repetitive patterns in the source file and such syndromes do not appear in encrypted files. Randomness is such an integral characteristic of encrypted files that an entropy test is often the basis for searching for encrypted files. Not all highly randomized files are encrypted, but the more random the contents of a file, the more likely that the file is encrypted. As an example,
AccessData's Forensic Toolkit (FTK), software widely used in the computer forensics field, uses the following tests to detect encrypted files: SIDEBAR: An 8-bit byte has 256 possible values. The entropy (E) of a binary file can be calculated using the following formula: where n=256 and P(xi) is the probability of a byte in this file having the value i. A small Perl program to compute the entropy of a file can be found at entropy.zip. Given this need for randomness, how do we ensure that crypto algorithms produce random numbers for high levels of entropy? Computers use random number generators (RNGs) for myriad purposes but computers cannot actually generate truly random sequences but, rather, sequences that have mostly random characteristics. To this end, computers use pseudorandom number generator (PRNG), aka deterministic random number generator, algorithms. NIST has a series of documents (SP 800-90: Random Bit Generators) that address this very issue:
The IETF's view of the randomness requirements for security can be found in RFC 4086. That paper notes several pitfalls when weak forms of entropy or traditional PRNG techniques are employed for purposes of security and cryptography. They also recommend the use of truly random hardware techniques and describe how existing systems can be used for these purposes. RFC 8937, produced by the Crypto Forum Research Group (CFRG), describes how security protocols can supplement their so-called "cryptographically secure" PRNG algorithms using long-term private keys.
Do not underestimate the importance of good random number generation to secure cryptography — and do not forget that an algorithm might be excellent but the implementation poor. Read, for example, "Millions of high-security crypto keys crippled by newly discovered flaw" (D. Goodin), which reported on a weakness in an RSA software library. Because RSA prime factorization arithmetic can be very complex on smart cards and other energy and memory constrained devices, the code for generating keys employed coding shortcuts. The result was that an attacker could calculate the private key from a vulnerable key-pair by only knowing the public key, which is totally anathema to the whole concept of public-key cryptography (i.e., the public key is supposed to be widely known without compromise of the private key). The vulnerability was due to the fact that the weakness was in the RNG and, therefore, a reduced level of randomness in the relationship between the private and public keys. This flaw, exposed in November 2017, had been present since at least 2012. For readers interested in learning more about information theory, see the following sites:
Finally, it is important to note that information theory is a continually evolving field. There is an area of research essentially questioning the "power" of entropy in determining the strength of a cryptosystem. An interesting paper about this is "Brute force searching, the typical set and Guesswork" by Christiansen, Duffy, du Pin Calmon, & Médard (2013 IEEE International Symposium on Information Theory); a relatively non-technical overview of that paper can be found at "Encryption is less secure than we hoped" by Gibbs (NetworkWorld, 08/16/2013). If you're going this far, also take a look at "Entropy as a Service: Unlocking Cryptography's Full Potential" (A. Vassilev & R. Staples, September 2016, Computer, 49(9), pp. 98-102). A.4. Cryptography in the Pre-Computer EraThis paper purposely focuses on cryptography terms, concepts, and schemes used in digital devices and is not a treatise of the whole field. No mention is made here about pre-computerized crypto schemes, the difference between a substitution and transposition cipher, cryptanalysis, or other history, nor is there a lot of theory presented here. That said, the history and evolution of cryptography is really interesting and readers should check out some of the books in the References and Further Reading section above. There are also several excellent Web sites that provide detailed information about the history of cryptographic methods, such as:
Finally, my software page contains a Perl program that implements several manual crypto schemes, including Caesar, Atbash, Vigenere Square, Beaufort, Myszkowski Transpostition, and ADFGVX ciphers. A.5. A Short Introduction to GroupsWithout a lot of explanation, I have made passing reference a few times in this paper to the concept of a group. In this section, I will give a very light introduction to some group theory. In mathematics, a group refers to a set of elements that can be combined by some operation. An important requirement is that when any two elements within the group are combined using the operation, the result is another element that is a member of the group. In that case, the group is said to be closed under that operation. So, by way of example, the set of positive integers ({1...∞}) is closed under addition because any two members of this group, when added, yields another member of the group. As a simple example, 3 and 18 are both members of the set of positive integers, as is their sum, 21. The sets of non-negative integers ({0...∞}) and all integers ({-∞...∞}, often denoted Z) are also closed under addition. These three groups are also closed under multiplication because, again, if you start with any two members of the set, their product is also a member of the set (e.g., 3 × 18 = 54). As it happens, these three groups are not all closed under subtraction. Consider that 3 - 18 = -15. This shows that Z is closed under subtraction, but the subsets of positive and non-negative integers are not. Finally, none of these sets are closed under division. Continuing with our friends, 3 and 18, we find that 3 ÷ 18 = 1/6 which is not a member of any set or subset of integers. So, continuing down this path just a bit more, let's take a look at the set of rational numbers. Rational numbers, usually denoted Q, are numbers that can be expressed as a fraction p/q, where p and q are integers and q≠0. The set of rational numbers is closed under division. As an example, consider two rational numbers, 5/6 and 11/12; dividing (5/6)/(11/12) yields a new rational number, namely 60/66 which can be reduced to 10/11. Irrational numbers, such as e, π, and √2, cannot be expressed as a simple fraction. APPENDIX B. ACRONYMS AND ABBREVIATIONS
Gary C. Kessler, Ph.D., CCE, CISSP, is the president and janitor of Gary Kessler Associates, a consulting, research, and training firm specializing in computer and network security (with a focus on maritime cybersecurity), computer forensics, and TCP/IP networking. He has written over 75 papers, articles, and book chapters for industry publications, is co-author of ISDN, 4th. edition (McGraw-Hill, 1998), a past editor-in-chief of the Journal of Digital Forensics, Security and Law, and co-author of Maritime Cybersecurity: A Guide for Leaders and Managers, 2/e (2022). Gary retired as Professor of Cybersecurity at Embry-Riddle Aeronautical University in Daytona Beach, Florida, and is an Adjunct Professor at Edith Cowan University in Perth, Western Australia. Gary was formerly an Associate Professor and Program Director of the M.S. in Information Assurance program at Norwich University in Northfield, Vermont, and a member of the Vermont Internet Crimes Against Children (ICAC) Task Force; he started the M.S. in Digital Investigation Management and undergraduate Computer & Digital Forensics programs at Champlain College in Burlington, Vermont. Gary's e-mail address is and his PGP public key can be found at https://www.garykessler.net/pubkey.html. Gary is also a SCUBA instructor and U.S. Coast Guard licensed captain. ACKNOWLEDGEMENTSThis section was introduced late in the life of this paper and so I apologize to any of you who have made helpful comments that remain unacknowledged. If you did make comments that I adopted — from catching typographical or factual errors to suggesting a new resource or topic — and I have failed to recognize you, please remind me! Thanks are offered to Steve Bellovin, Sitaram Chamarty, DidiSoft, Bernhard Esslinger (and his students at the University of Siegen, Germany, contributors to the CrypTool project), William R. Godwin, Craig Heilman, Luveh Keraph, Robert Litts, Hugh Macdonald, Douglas P. McNutt, Marcin Olak, Josh Silman, Barry Steyn, and Miles Wolbe. What is another term for a cryptographic algorithm?Cryptosystems use a set of procedures known as cryptographic algorithms, or ciphers, to encrypt and decrypt messages to secure communications among computer systems, devices and applications. A cipher suite uses one algorithm for encryption, another algorithm for message authentication and another for key exchange.
What is the alternative name of symmetric cryptography?Symmetric cryptography, known also as secret key cryptography, is the use of a single shared secret to share encrypted data between parties.
Which of the following is asymmetric cryptography algorithm?RSA is an algorithm used by modern computers to encrypt and decrypt messages. It is an asymmetric cryptographic algorithm.
Which asymmetric cryptography algorithms is most commonly used?RSA Asymmetric Encryption Algorithm
Invented by Ron Rivest, Adi Shamir, and Leonard Adleman (hence “RSA”) in 1977, RSA is, to date, the most widely used asymmetric encryption algorithm.
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