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Ä Area: sci.crypt ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ Msg#: 20302 Date: 08-04-94 08:18 From: News Read: Yes Replied: No To: All Mark: Subj: CRYPTOGRAPHY FAQ (01/10: ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ Xref: netcomsv sci.crypt:28416 talk.politics.crypto:6758 sci.answers:1398 news.answers:26003 talk.answers:295 Path: netcomsv!netcomsv!decwrl!enews.sgi.com!ames!elroy.jpl.nasa.gov!usc!bloom-beacon .mit.edu!senator-bedfellow.mit.edu!faqserv From: crypt-comments@math.ncsu.edu Newsgroups: sci.crypt,talk.politics.crypto,sci.answers,news.answers,talk.answers Subject: Cryptography FAQ (01/10: Overview) Supersedes: <cryptography-faq/part01_773577928@rtfm.mit.edu> Followup-To: poster Date: 30 Jul 1994 05:11:16 GMT Organization: The Crypt Cabal Lines: 152 Approved: news-answers-request@MIT.Edu Expires: 3 Sep 1994 05:10:33 GMT Message-ID: <cryptography-faq/part01_775545033@rtfm.mit.edu> Reply-To: crypt-comments@math.ncsu.edu NNTP-Posting-Host: bloom-picayune.mit.edu Summary: Part 1 of 10 of the sci.crypt FAQ, Overview. Table of contents, contributors, feedback, archives, administrivia, changes. X-Last-Updated: 1994/07/05 Originator: faqserv@bloom-picayune.MIT.EDU Archive-name: cryptography-faq/part01 Version: 1.0 Last-modified: 94/01/11 This is the first of ten parts of the sci.crypt FAQ. The parts are mostly independent, but you should read this part before the rest. We don't have the time to send out missing parts by mail, so don't ask. Notes such as ``[KAH67]'' refer to the reference list in the last part. Disclaimer: This document is the product of the Crypt Cabal, a secret society which serves the National Secu---uh, no. Seriously, we're the good guys, and we've done what we can to ensure the completeness and accuracy of this document, but in a field of military and commercial importance like cryptography you have to expect that some people and organizations consider their interests more important than open scientific discussion. Trust only what you can verify firsthand. And don't sue us. Many people have contributed to this FAQ. In alphabetical order: Eric Bach, Steve Bellovin, Dan Bernstein, Nelson Bolyard, Carl Ellison, Jim Gillogly, Mike Gleason, Doug Gwyn, Luke O'Connor, Tony Patti, William Setzer. We apologize for any omissions. If you have suggestions, comments, or criticism, please let the current editors know by sending e-mail to crypt-comments@math.ncsu.edu. Bear in mind that this is a work in progress; there are some questions which we should add but haven't gotten around to yet. In making comments on additions it is most helpful if you are as specific as possible and ideally even provide the actual exact text. Archives: sci.crypt has been archived since October 1991 on ripem.msu.edu, though these archives are available only to U.S. and Canadian users. Another site is rpub.cl.msu.edu in /pub/crypt/sci.crypt/ from Jan 1992. Please contact crypt-comments@math.ncsu.edu if you know of other archives. The sections of this FAQ are available via anonymous FTP to rtfm.mit.edu as /pub/usenet/news.answers/cryptography-faq/part[xx]. The Cryptography FAQ is posted to the newsgroups sci.crypt, talk.politics.crypto, sci.answers, and news.answers every 21 days. The fields `Last-modified' and `Version' at the top of each part track revisions. Table of Contents ----------------- 1. Overview 2. Net Etiquette 2.1. What groups are around? What's a FAQ? Who am I? Why am I here? 2.2. Do political discussions belong in sci.crypt? 2.3. How do I present a new encryption scheme in sci.crypt? 3. Basic Cryptology 3.1. What is cryptology? Cryptography? Plaintext? Ciphertext? Encryption? Key? 3.2. What references can I start with to learn cryptology? 3.3. How does one go about cryptanalysis? 3.4. What is a brute-force search and what is its cryptographic relevance? 3.5. What are some properties satisfied by every strong cryptosystem? 3.6. If a cryptosystem is theoretically unbreakable, then is it guaranteed analysis-proof in practice? 3.7. Why are many people still using cryptosystems that are relatively easy to break? 3.8. What are the basic types of cryptanalytic `attacks'? 4. Mathematical Cryptology 4.1. In mathematical terms, what is a private-key cryptosystem? 4.2. What is an attack? 4.3. What's the advantage of formulating all this mathematically? 4.4. Why is the one-time pad secure? 4.5. What's a ciphertext-only attack? 4.6. What's a known-plaintext attack? 4.7. What's a chosen-plaintext attack? 4.8. In mathematical terms, what can you say about brute-force attacks? 4.9. What's a key-guessing attack? What's entropy? 5. Product Ciphers 5.1. What is a product cipher? 5.2. What makes a product cipher secure? 5.3. What are some group-theoretic properties of product ciphers? 5.4. What can be proven about the security of a product cipher? 5.5. How are block ciphers used to encrypt data longer than the block size? 5.6. Can symmetric block ciphers be used for message authentication? 5.7. What exactly is DES? 5.8. What is triple DES? 5.9. What is differential cryptanalysis? 5.10. How was NSA involved in the design of DES? 5.11. Is DES available in software? 5.12. Is DES available in hardware? 5.13. Can DES be used to protect classified information? 5.14. What are ECB, CBC, CFB, and OFB encryption? 6. Public-Key Cryptography 6.1. What is public-key cryptography? 6.2. How does public-key cryptography solve cryptography's Catch-22? 6.3. What is the role of the `trapdoor function' in public key schemes? 6.4. What is the role of the `session key' in public key schemes? 6.5. What's RSA? 6.6. Is RSA secure? 6.7. What's the difference between the RSA and Diffie-Hellman schemes? 6.8. What is `authentication' and the `key distribution problem'? 6.9. How fast can people factor numbers? 6.10. What about other public-key cryptosystems? 6.11. What is the `RSA Factoring Challenge?' 7. Digital Signatures 7.1. What is a one-way hash function? 7.2. What is the difference between public, private, secret, shared, etc.? 7.3. What are MD4 and MD5? 7.4. What is Snefru? 8. Technical Miscellany 8.1. How do I recover from lost passwords in WordPerfect? 8.2. How do I break a Vigenere (repeated-key) cipher? 8.3. How do I send encrypted mail under UNIX? [PGP, RIPEM, PEM, ...] 8.4. Is the UNIX crypt command secure? 8.5. How do I use compression with encryption? 8.6. Is there an unbreakable cipher? 8.7. What does ``random'' mean in cryptography? 8.8. What is the unicity point (a.k.a. unicity distance)? 8.9. What is key management and why is it important? 8.10. Can I use pseudo-random or chaotic numbers as a key stream? 8.11. What is the correct frequency list for English letters? 8.12. What is the Enigma? 8.13. How do I shuffle cards? 8.14. Can I foil S/W pirates by encrypting my CD-ROM? 8.15. Can you do automatic cryptanalysis of simple ciphers? 8.16. What is the coding system used by VCR+? 9. Other Miscellany 9.1. What is the National Security Agency (NSA)? 9.2. What are the US export regulations? 9.3. What is TEMPEST? 9.4. What are the Beale Ciphers, and are they a hoax? 9.5. What is the American Cryptogram Association, and how do I get in touch? 9.6. Is RSA patented? 9.7. What about the Voynich manuscript? 10. References 10.1. Books on history and classical methods 10.2. Books on modern methods 10.3. Survey articles 10.4. Reference articles 10.5. Journals, conference proceedings 10.6. Other 10.7. How may one obtain copies of FIPS and ANSI standards cited herein? 10.8. Electronic sources 10.9. RFCs (available from [FTPRF]) 10.10. Related newsgroups This is the second of ten parts of the sci.crypt FAQ. The parts are mostly independent, but you should read the first part before the rest. We don't have the time to send out missing parts by mail, so don't ask. Notes such as ``[KAH67]'' refer to the reference list in the last part. The sections of this FAQ are available via anonymous FTP to rtfm.mit.edu as /pub/usenet/news.answers/cryptography-faq/part[xx]. The Cryptography FAQ is posted to the newsgroups sci.crypt, talk.politics.crypto, sci.answers, and news.answers every 21 days. Contents: 2.1. What groups are around? What's a FAQ? Who am I? Why am I here? 2.2. Do political discussions belong in sci.crypt? 2.3. How do I present a new encryption scheme in sci.crypt? 2.1. What groups are around? What's a FAQ? Who am I? Why am I here? Read news.announce.newusers and news.answers for a few weeks. Always make sure to read a newsgroup for some time before you post to it. You'll be amazed how often the same question can be asked in the same newsgroup. After a month you'll have a much better sense of what the readers want to see. 2.2. Do political discussions belong in sci.crypt? No. In fact some newsgroups (notably misc.legal.computing) were created exactly so that political questions like ``Should RSA be patented?'' don't get in the way of technical discussions. Many sci.crypt readers also read misc.legal.computing, comp.org.eff.talk, comp.patents, sci.math, comp.compression, talk.politics.crypto, et al.; for the benefit of people who don't care about those other topics, try to put your postings in the right group. Questions about microfilm and smuggling and other non-cryptographic ``spy stuff'' don't belong in sci.crypt either. 2.3. How do I present a new encryption scheme in sci.crypt? ``I just came up with this neat method of encryption. Here's some ciphertext: FHDSIJOYW^&%$*#@OGBUJHKFSYUIRE. Is it strong?'' Without a doubt questions like this are the most annoying traffic on sci.crypt. If you have come up with an encryption scheme, providing some ciphertext from it is not adequate. Nobody has ever been impressed by random gibberish. Any new algorithm should be secure even if the opponent knows the full algorithm (including how any message key is distributed) and only the private key is kept secret. There are some systematic and unsystematic ways to take reasonably long ciphertexts and decrypt them even without prior knowledge of the algorithm, but this is a time-consuming and possibly fruitless exercise which most sci.crypt readers won't bother with. So what do you do if you have a new encryption scheme? First of all, find out if it's really new. Look through this FAQ for references and related methods. Familiarize yourself with the literature and the introductory textbooks. When you can appreciate how your cryptosystem fits into the world at large, try to break it yourself! You shouldn't waste the time of tens of thousands of readers asking a question which you could have easily answered on your own. If you really think your system is secure, and you want to get some reassurance from experts, you might try posting full details of your system, including working code and a solid theoretical explanation, to sci.crypt. (Keep in mind that the export of cryptography is regulated in some areas.) If you're lucky an expert might take some interest in what you posted. You can encourage this by offering cash rewards---for instance, noted cryptographer Ralph Merkle is offering $1000 to anyone who can break Snefru-4---but there are no guarantees. If you don't have enough experience, then most likely any experts who look at your system will be able to find a flaw. If this happens, it's your responsibility to consider the flaw and learn from it, rather than just add one more layer of complication and come back for another round. A different way to get your cryptosystem reviewed is to have the NSA look at it. A full discussion of this procedure is outside the scope of this FAQ. Among professionals, a common rule of thumb is that if you want to design a cryptosystem, you have to have experience as a cryptanalyst. This is the third of ten parts of the sci.crypt FAQ. The parts are mostly independent, but you should read the first part before the rest. We don't have the time to send out missing parts by mail, so don't ask. Notes such as ``[KAH67]'' refer to the reference list in the last part. The sections of this FAQ are available via anonymous FTP to rtfm.mit.edu as /pub/usenet/news.answers/cryptography-faq/part[xx]. The Cryptography FAQ is posted to the newsgroups sci.crypt, talk.politics.crypto, sci.answers, and news.answers every 21 days. Contents: 3.1. What is cryptology? Cryptography? Plaintext? Ciphertext? Encryption? Key? 3.2. What references can I start with to learn cryptology? 3.3. How does one go about cryptanalysis? 3.4. What is a brute-force search and what is its cryptographic relevance? 3.5. What are some properties satisfied by every strong cryptosystem? 3.6. If a cryptosystem is theoretically unbreakable, then is it guaranteed analysis-proof in practice? 3.7. Why are many people still using cryptosystems that are relatively easy to break? 3.8. What are the basic types of cryptanalytic `attacks'? 3.1. What is cryptology? Cryptography? Plaintext? Ciphertext? Encryption? Key? The story begins: When Julius Caesar sent messages to his trusted acquaintances, he didn't trust the messengers. So he replaced every A by a D, every B by a E, and so on through the alphabet. Only someone who knew the ``shift by 3'' rule could decipher his messages. A cryptosystem or cipher system is a method of disguising messages so that only certain people can see through the disguise. Cryptography is the art of creating and using cryptosystems. Cryptanalysis is the art of breaking cryptosystems---seeing through the disguise even when you're not supposed to be able to. Cryptology is the study of both cryptography and cryptanalysis. The original message is called a plaintext. The disguised message is called a ciphertext. Encryption means any procedure to convert plaintext into ciphertext. Decryption means any procedure to convert ciphertext into plaintext. A cryptosystem is usually a whole collection of algorithms. The algorithms are labelled; the labels are called keys. For instance, Caesar probably used ``shift by n'' encryption for several different values of n. It's natural to say that n is the key here. The people who are supposed to be able to see through the disguise are called recipients. Other people are enemies, opponents, interlopers, eavesdroppers, or third parties. 3.2. What references can I start with to learn cryptology? For an introduction to technical matter, the survey articles given in part 10 are the best place to begin as they are, in general, concise, authored by competent people, and well written. However, these articles are mostly concerned with cryptology as it has developed in the last 50 years or so, and are more abstract and mathematical than historical. The Codebreakers by Kahn [KAH67] is encyclopedic in its history and technical detail of cryptology up to the mid-60's. Introductory cryptanalysis can be learned from Gaines [GAI44] or Sinkov [SIN66]. This is recommended especially for people who want to devise their own encryption algorithms since it is a common mistake to try to make a system before knowing how to break one. The selection of an algorithm for the DES drew the attention of many public researchers to problems in cryptology. Consequently several textbooks and books to serve as texts have appeared. The book of Denning [DEN82] gives a good introduction to a broad range of security including encryption algorithms, database security, access control, and formal models of security. Similar comments apply to the books of Price & Davies [PRI84] and Pfleeger [PFL89]. The books of Konheim [KON81] and Meyer & Matyas [MEY82] are quite technical books. Both Konheim and Meyer were directly involved in the development of DES, and both books give a thorough analysis of DES. Konheim's book is quite mathematical, with detailed analyses of many classical cryptosystems. Meyer and Matyas concentrate on modern cryptographic methods, especially pertaining to key management and the integration of security facilities into computer systems and networks. For more recent documentation on related areas, try G. Simmons in [SIM91]. The books of Rueppel [RUE86] and Koblitz [KOB89] concentrate on the application of number theory and algebra to cryptography. 3.3. How does one go about cryptanalysis? Classical cryptanalysis involves an interesting combination of analytical reasoning, application of mathematical tools, pattern finding, patience, determination, and luck. The best available textbooks on the subject are the Military Cryptanalytics series [FRIE1]. It is clear that proficiency in cryptanalysis is, for the most part, gained through the attempted solution of given systems. Such experience is considered so valuable that some of the cryptanalyses performed during WWII by the Allies are still classified. Modern public-key cryptanalysis may consist of factoring an integer, or taking a discrete logarithm. These are not the traditional fare of the cryptanalyst. Computational number theorists are some of the most successful cryptanalysts against public key systems. 3.4. What is a brute-force search and what is its cryptographic relevance? In a nutshell: If f(x) = y and you know y and can compute f, you can find x by trying every possible x. That's brute-force search. Example: Say a cryptanalyst has found a plaintext and a corresponding ciphertext, but doesn't know the key. He can simply try encrypting the plaintext using each possible key, until the ciphertext matches---or decrypting the ciphertext to match the plaintext, whichever is faster. Every well-designed cryptosystem has such a large key space that this brute-force search is impractical. Advances in technology sometimes change what is considered practical. For example, DES, which has been in use for over 10 years now, has 2^56, or about 10^17, possible keys. A computation with this many operations was certainly unlikely for most users in the mid-70's. The situation is very different today given the dramatic decrease in cost per processor operation. Massively parallel machines threaten the security of DES against brute force search. Some scenarios are described by Garron and Outerbridge [GAR91]. One phase of a more sophisticated cryptanalysis may involve a brute-force search of some manageably small space of possibilities. 3.5. What are some properties satisfied by every strong cryptosystem? The security of a strong system resides with the secrecy of the key rather than with the supposed secrecy of the algorithm. A strong cryptosystem has a large keyspace, as mentioned above. It has a reasonably large unicity distance; see question 8.8. A strong cryptosystem will certainly produce ciphertext which appears random to all standard statistical tests (see, for example, [CAE90]). A strong cryptosystem will resist all known previous attacks. A system which has never been subjected to scrutiny is suspect. If a system passes all the tests mentioned above, is it necessarily strong? Certainly not. Many weak cryptosystems looked good at first. However, sometimes it is possible to show that a cryptosystem is strong by mathematical proof. ``If Joe can break this system, then he can also solve the well-known difficult problem of factoring integers.'' See part 6. Failing that, it's a crap shoot. 3.6. If a cryptosystem is theoretically unbreakable, then is it guaranteed analysis-proof in practice? Cryptanalytic methods include what is known as ``practical cryptanalysis'': the enemy doesn't have to just stare at your ciphertext until he figures out the plaintext. For instance, he might assume ``cribs''---stretches of probable plaintext. If the crib is correct then he might be able to deduce the key and then decipher the rest of the message. Or he might exploit ``isologs''---the same plaintext enciphered in several cryptosystems or several keys. Thus he might obtain solutions even when cryptanalytic theory says he doesn't have a chance. Sometimes, cryptosystems malfunction or are misused. The one-time pad, for example, loses all security if it is used more than once! Even chosen-plaintext attacks, where the enemy somehow feeds plaintext into the encryptor until he can deduce the key, have been employed. See [KAH67]. 3.7. Why are many people still using cryptosystems that are relatively easy to break? Some don't know any better. Often amateurs think they can design secure systems, and are not aware of what an expert cryptanalyst could do. And sometimes there is insufficient motivation for anybody to invest the work needed to crack a system. 3.8. What are the basic types of cryptanalytic `attacks'? A standard cryptanalytic attack is to know some plaintext matching a given piece of ciphertext and try to determine the key which maps one to the other. This plaintext can be known because it is standard (a standard greeting, a known header or trailer, ...) or because it is guessed. If text is guessed to be in a message, its position is probably not known, but a message is usually short enough that the cryptanalyst can assume the known plaintext is in each possible position and do attacks for each case in parallel. In this case, the known plaintext can be something so common that it is almost guaranteed to be in a message. A strong encryption algorithm will be unbreakable not only under known plaintext (assuming the enemy knows all the plaintext for a given ciphertext) but also under "adaptive chosen plaintext" -- an attack making life much easier for the cryptanalyst. In this attack, the enemy gets to choose what plaintext to use and gets to do this over and over, choosing the plaintext for round N+1 only after analyzing the result of round N. For example, as far as we know, DES is reasonably strong even under an adaptive chosen plaintext attack (the attack Biham and Shamir used). Of course, we do not have access to the secrets of government cryptanalytic services. Still, it is the working assumption that DES is reasonably strong under known plaintext and triple-DES is very strong under all attacks. To summarize, the basic types of cryptanalytic attacks in order of difficulty for the attacker, hardest first, are: cyphertext only: the attacker has only the encoded message from which to determine the plaintext, with no knowledge whatsoever of the latter. A cyphertext only attack is usually presumed to be possible, and a code's resistance to it is considered the basis of its cryptographic security. known plaintext: the attacker has the plaintext and corresponding cyphertext of an arbitrary message not of his choosing. The particular message of the sender's is said to be `compromised'. In some systems, one known cyphertext-plaintext pair will compromise the overall system, both prior and subsequent transmissions, and resistance to this is characteristic of a secure code. Under the following attacks, the attacker has the far less likely or plausible ability to `trick' the sender into encrypting or decrypting arbitrary plaintexts or cyphertexts. Codes that resist these attacks are considered to have the utmost security. chosen plaintext: the attacker has the capability to find the cyphertext corresponding to an arbitrary plaintext message of his choosing. chosen cyphertext: the attacker can choose arbitrary cyphertext and find the corresponding decrypted plaintext. This attack can show in public key systems, where it may reveal the private key. adaptive chosen plaintext: the attacker can determine the cyphertext of chosen plaintexts in an interactive or iterative process based on previous results. This is the general name for a method of attacking product ciphers called `differential cryptanalysis'. The next part of the FAQ gives the mathematical detail behind the various types of cryptoanalytic attacks. This is the fourth of ten parts of the sci.crypt FAQ. The parts are mostly independent, but you should read the first part before the rest. We don't have the time to send out missing parts by mail, so don't ask. Notes such as ``[KAH67]'' refer to the reference list in the last part. The sections of this FAQ are available via anonymous FTP to rtfm.mit.edu as /pub/usenet/news.answers/cryptography-faq/part[xx]. The Cryptography FAQ is posted to the newsgroups sci.crypt, talk.politics.crypto, sci.answers, and news.answers every 21 days. Contents: 4.1. In mathematical terms, what is a private-key cryptosystem? 4.2. What is an attack? 4.3. What's the advantage of formulating all this mathematically? 4.4. Why is the one-time pad secure? 4.5. What's a ciphertext-only attack? 4.6. What's a known-plaintext attack? 4.7. What's a chosen-plaintext attack? 4.8. In mathematical terms, what can you say about brute-force attacks? 4.9. What's a key-guessing attack? What's entropy? Reader, beware: This section is highly mathematical. Well, maybe not _highly_ mathematical, but it's got a bunch of symbols and scary-looking formulas. You have been warned. 4.1. In mathematical terms, what is a private-key cryptosystem? A private-key cryptosystem consists of an encryption system E and a decryption system D. The encryption system E is a collection of functions E_K, indexed by ``keys'' K, mapping some set of ``plaintexts'' P to some set of ``ciphertexts'' C. Similarly the decryption system D is a collection of functions D_K such that D_K(E_K(P)) = P for every plaintext P. That is, succesful decryption of ciphertext into plaintext is accomplished using the same key (index) as was used for the corresponding encryption of plaintext into ciphertext. Such systems, where the same key value is used to encrypt and decrypt, are also known as ``symmetric'' cryptoystems. 4.2. What is an attack? In intuitive terms a (passive) attack on a cryptosystem is any method of starting with some information about plaintexts and their corresponding ciphertexts under some (unknown) key, and figuring out more information about the plaintexts. It's possible to state mathematically what this means. Here we go. Fix functions F, G, and H of n variables. Fix an encryption system E, and fix a distribution of plaintexts and keys. An attack on E using G assuming F giving H with probability p is an algorithm A with a pair f, g of inputs and one output h, such that there is probability p of computing h = H(P_1,...,P_n), if we have f = F(P_1,...,P_n) and g = G(E_K(P_1),...,E_K(P_n)). Note that this probability depends on the distribution of the vector (K,P_1,...,P_n). The attack is trivial (or ``pointless'') if there is probability at least p of computing h = H(P_1,...,P_n) if f = F(P_1,...,P_n) and g = G(C_1,...,C_n). Here C_1,...,C_n range uniformly over the possible ciphertexts, and have no particular relation to P_1,...,P_n. In other words, an attack is trivial if it doesn't actually use the encryptions E_K(P_1),...,E_K(P_n). An attack is called ``one-ciphertext'' if n = 1, ``two-ciphertext'' if n = 2, and so on. 4.3. What's the advantage of formulating all this mathematically? In basic cryptology you can never prove that a cryptosystem is secure. Read part 3: we keep saying ``a strong cryptosystem must have this property, but having this property is no guarantee that a cryptosystem is strong!'' In contrast, the purpose of mathematical cryptology is to precisely formulate and, if possible, prove the statement that a cryptosystem is strong. We say, for example, that a cryptosystem is secure against all (passive) attacks if any nontrivial attack against the system (as defined above) is too slow to be practical. If we can prove this statement then we have confidence that our cryptosystem will resist any (passive) cryptanalytic technique. If we can reduce this statement to some well-known unsolved problem then we still have confidence that the cryptosystem isn't easy to break. Other parts of cryptology are also amenable to mathematical definition. Again the point is to explicitly identify what assumptions we're making and prove that they produce the desired results. We can figure out what it means for a particular cryptosystem to be used properly: it just means that the assumptions are valid. The same methodology is useful for cryptanalysis too. The cryptanalyst can take advantage of incorrect assumptions. Often he can try to construct a proof of security for a system, see where the proof fails, and use these failures as the starting points for his analysis. 4.4. Why is the one-time pad secure? By definition, the one-time pad is a cryptosystem where the plaintexts, ciphertexts, and keys are all strings (say byte strings) of some length m, and E_K(P) is just the sum (let's say the exclusive or) of K and P. It is easy to prove mathematically that there are _no_ nontrivial single-ciphertext attacks on the one-time pad, assuming a uniform distribution of keys. Note that we don't have to assume a uniform distribution of plaintexts. (Here's the proof: Let A be an attack, i.e., an algorithm taking two inputs f, g and producing one output h, with some probability p that h = H(P) whenever f = F(P) and g = G(E_K(P)) (i.e., g = G(K + P)). Then, because the distribution of K is uniform and independent of P, the distribution of K + P must also be uniform and independent of P. But also the distribution of C is uniform and independent of P. Hence there is probability exactly p that h = H(P) whenever f = F(P) and g = G(C), over all P and C. Thus a fortiori A is trivial.) On the other hand the one-time pad is _not_ secure if a key K is used for more than one plaintext: i.e., there are nontrivial multiple-ciphertext attacks. So to be properly used a key K must be thrown away after one encryption. The key is also called a ``pad''; this explains the name ``one-time pad.'' Also, a computer-based pseudo-random number generator does _not_ qualify as a true one-time pad because of its deterministic properties. See `pseudo-random number generators as key stream'. 4.5. What's a ciphertext-only attack? In the notation above, a ciphertext-only attack is one where F is constant. Given only some information G(E_K(P_1),...,E_K(P_n)) about n ciphertexts, the attack has to have some chance of producing some information H(P_1,...,P_n) about the plaintexts. The attack is trivial if it has just as good a chance of producing H(P_1,...,P_n) when given G(C_1,...,C_n) for random C_1,...,C_n. For example, say G(C) = C, and say H(P) is the first bit of P. We can easily write down an attack---the ``guessing attack,'' which simply guesses that H(P) is 1. This attack is trivial because it doesn't use the ciphertext: it has a fifty-fifty chance of guessing correctly no matter what. On the other hand there is an attack on RSA which produces one bit of information about P, with 100% success, using C. If it is fed a random C then the success rate drops to 50%. So this is a nontrivial attack. 4.6. What's a known-plaintext attack? The classic known-plaintext attack has F(P_1,P_2) = P_1, G(C_1,C_2) = (C_1,C_2), and H(P_1,P_2) depending only on P_2. In other words, given two ciphertexts C_1 and C_2 and one decryption P_1, the known-plaintext attack should produce information about the other decryption P_2. Note that known-plaintext attacks are often defined in the literature as producing information about the key, but this is pointless: the cryptanalyst generally cares about the key only insofar as it lets him decrypt further messages. 4.7. What's a chosen-plaintext attack? A chosen-plaintext attack is the first of an increasingly impractical series of _active_ attacks on a cryptosystem: attacks where the cryptanalyst feeds data to the encryptor. These attacks don't fit into our model of passive attacks explained above. Anyway, a chosen-plaintext attack lets the cryptanalyst choose a plaintext and look at the corresponding ciphertext, then repeat until he has figured out how to decrypt any message. More absurd examples of this sort of attack are the ``chosen-key attack'' and ``chosen-system attack.'' A much more important form of active attack is a message corruption attack, where the attacker tries to change the ciphertext in such a way as to make a useful change in the plaintext. There are many easy ways to throw kinks into all of these attacks: for instance, automatically encrypting any plaintext P as T,E_K(h(T+R+P),R,P), where T is a time-key (sequence number) chosen anew for each message, R is a random number, and h is a one-way hash function. Here comma means concatenation and plus means exclusive-or. 4.8. In mathematical terms, what can you say about brute-force attacks? Consider the following known-plaintext attack. We are given some plaintexts P_1,...,P_{n-1} and ciphertexts C_1,...,C_{n-1}. We're also given a ciphertext C_n. We run through every key K. When we find K such that E_K(P_i) = C_i for every i < n, we print D_K(C_n). If n is big enough that only one key works, this attack will succeed on valid inputs all the time, while it will produce correct results only once in a blue moon for random inputs. Thus this is a nontrivial attack. Its only problem is that it is very slow if there are many possible keys. 4.9. What's a key-guessing attack? What's entropy? Say somebody is using the one-time pad---but isn't choosing keys randomly and uniformly from all m-bit messages, as he was supposed to for our security proof. In fact say he's known to prefer keys which are English words. Then a cryptanalyst can run through all English words as possible keys. This attack will often succeed, and it's much faster than a brute-force search of the entire keyspace. We can measure how bad a key distribution is by calculating its entropy. This number E is the number of ``real bits of information'' of the key: a cryptanalyst will typically happen across the key within 2^E guesses. E is defined as the sum of -p_K log_2 p_K, where p_K is the probability of key K. This is the fifth of ten parts of the sci.crypt FAQ. The parts are mostly independent, but you should read the first part before the rest. We don't have the time to send out missing parts by mail, so don't ask. Notes such as ``[KAH67]'' refer to the reference list in the last part. The sections of this FAQ are available via anonymous FTP to rtfm.mit.edu as /pub/usenet/news.answers/cryptography-faq/part[xx]. The Cryptography FAQ is posted to the newsgroups sci.crypt, talk.politics.crypto, sci.answers, and news.answers every 21 days. Contents: 5.1. What is a product cipher? 5.2. What makes a product cipher secure? 5.3. What are some group-theoretic properties of product ciphers? 5.4. What can be proven about the security of a product cipher? 5.5. How are block ciphers used to encrypt data longer than the block size? 5.6. Can symmetric block ciphers be used for message authentication? 5.7. What exactly is DES? 5.8. What is triple DES? 5.9. What is differential cryptanalysis? 5.10. How was NSA involved in the design of DES? 5.11. Is DES available in software? 5.12. Is DES available in hardware? 5.13. Can DES be used to protect classified information? 5.14. What are ECB, CBC, CFB, OFB, and PCBC encryption? 5.1. What is a product cipher? A product cipher is a block cipher that iterates several weak operations such as substitution, transposition, modular addition/multiplication, and linear transformation. (A ``block cipher'' just means a cipher that encrypts a block of data---8 bytes, say---all at once, then goes on to the next block.) The notion of product ciphers is due to Shannon [SHA49]. Examples of modern product ciphers include LUCIFER [SOR84], DES [NBS77], SP-networks [KAM78], LOKI [BRO90], FEAL [SHI84], PES [LAI90], Khufu and Khafre [ME91a]. The so-called Feistel ciphers are a class of product ciphers which operate on one half of the ciphertext at each round, and then swap the ciphertext halves after each round. LUCIFER, DES, LOKI, and FEAL are examples of Feistel ciphers. The following table compares the main parameters of several product ciphers: cipher | block length | key bits | number of rounds LUCIFER 128 128 16 DES 64 56 16 LOKI 64 64 16 FEAL 64 128 2^x, x >= 5 PES 64 128 8 5.2. What makes a product cipher secure? Nobody knows how to prove mathematically that a product cipher is completely secure. So in practice one begins by demonstrating that the cipher ``looks highly random''. For example, the cipher must be nonlinear, and it must produce ciphertext which functionally depends on every bit of the plaintext and the key. Meyer [MEY78] has shown that at least 5 rounds of DES are required to guarantee such a dependence. In this sense a product cipher should act as a ``mixing'' function which combines the plaintext, key, and ciphertext in a complex nonlinear fashion. The fixed per-round substitutions of the product cipher are referred to as S-boxes. For example, LUCIFER has 2 S-boxes, and DES has 8 S-boxes. The nonlinearity of a product cipher reduces to a careful design of these S-boxes. A list of partial design criteria for the S-boxes of DES, which apply to S-boxes in general, may be found in Brown [BRO89] and Brickell et al. [BRI86]. 5.3. What are some group-theoretic properties of product ciphers? Let E be a product cipher that maps N-bit blocks to N-bit blocks. Let E_K(X) be the encryption of X under key K. Then, for any fixed K, the map sending X to E_K(X) is a permutation of the set of N-bit blocks. Denote this permutation by P_K. The set of all N-bit permutations is called the symmetric group and is written S_{2^N}. The collection of all these permutations P_K, where K ranges over all possible keys, is denoted E(S_{2^N}). If E were a random mapping from plaintexts to ciphertexts then we would expect E(S_{2^N}) to generate a large subset of S_{2^N}. Coppersmith and Grossman [COP74] have shown that a very simple product cipher can generate the alternating group A_{2^N} given a sufficient number of rounds. (The alternating group is half of the symmetric group: it consists of all ``even'' permutations, i.e., all permutations which can be written as an even number of swaps.) Even and Goldreich [EVE83] were able to extend these results to show that Feistel ciphers can generate A_{2^N}, given a sufficient number of rounds. The security of multiple encipherment also depends on the group-theoretic properties of a cipher. Multiple encipherment is an extension over single encipherment if for keys K1, K2 there does not exist a third key K3 such that E_K2(E_K1(X)) == E_(K3)(X) (**) which indicates that encrypting twice with two independent keys K1, K2 is equal to a single encryption under the third key K3. If for every K1, K2 there exists a K3 such that eq. (**) is true then we say that E is a group. This question of whether DES is a group under this definition was extensively studied by Sherman, Kaliski, and Rivest [SHE88]. In their paper they give strong evidence for the hypothesis that DES is not a group. In fact DES is not a group [CAM93]. 5.4. What can be proven about the security of a product cipher? Recall from above that P_K is a permutation produced by E under some key K. The goal of the designer of E is to ensure that P_K appears to be a random element of S_{2^N}, the symmetric group. Let R be an element of S_{2^N} selected randomly. We will say that P_K and R are indistinguishable if an observer given P_K and R in some order cannot distinguish between these two permutations in polynomial time. That is, with time bounded resources, the observer cannot determine which of the permutations is produced by E: the optimal decision is no better than simply guessing. Luby and Rackoff [LUB88] have shown that a class of Feistel ciphers are secure in this sense when the round mapping is replaced by random boolean functions. 5.5. How are block ciphers used to encrypt data longer than the block size? There are four standard ``modes of operation'' (and numerous non-standard ones as well). The standard modes of operation are defined in the U.S. Department of Commerce Federal Information Processing Standard (FIPS) 81, published in 1980. See the question about ECB below for more details. Although they are defined for the DES block cipher, the ``modes of operation'' can be used with any block cipher. 5.6. Can symmetric block ciphers be used for message authentication? You may use a symmetric cryptosystem block cipher to prove to yourself that you generated a message, and that the message wasn't altered after you created it. But you cannot prove these things to anyone else without revealing your key. Thereafter you cannot prove anything about messages authenticated with that key. See ANSI X3.106-1983 and FIPS 113 (1985) for a standard method of message authentication using DES. 5.7. What exactly is DES? DES is the U.S. Government's Data Encryption Standard, a product cipher that operates on 64-bit blocks of data, using a 56-bit key. It is defined in FIPS 46-1 (1988) [which supersedes FIPS 46 (1977)]. FIPS are Federal Information Processing Standards published by NTIS. DES is identical to the ANSI standard Data Encryption Algorithm (DEA) defined in ANSI X3.92-1981. 5.8. What is triple DES? Triple DES is a product cipher which, like DES, operates on 64-bit data blocks. There are several forms, each of which uses the DES cipher 3 times. Some forms use two 56-bit keys, some use three. The DES ``modes of operation'' may also be used with triple-DES. Some people refer to E(K1,D(K2,E(K1,x))) as triple-DES. This method is defined in chapter 7.2 of the ANSI standard X9.17-1985 ``Financial Institution Key Management'' and is intended for use in encrypting DES keys and IVs for ``Automated Key Distribution''. Its formal name is ``Encryption and Decryption of a Single Key by a Key Pair'', but it is referenced in other standards documents as EDE. That standard says (section 7.2.1): ``Key encrypting keys may be a single DEA key or a DEA key pair. Key pairs shoud be used where additional security is needed (e.g., the data protected by the key(s) has a long security life). A key pair shall not be encrypted or decrypted using a single key.'' Others use the term ``triple-DES'' for E(K1,D(K2,E(K3,x))) or E(K1,E(K2,E(K3,x))). All of these methods are defined only for ECB mode of operation. The security of various methods of achieving other modes of operation (such as CBC) is under study at the moment. For now, it should be assumed that other modes be defined as they are today, but with E(K1,D(K2,E(K1,x))) as the block cipher within the feedback mechanism creating the mode. One of us (Ellison) has long advocated triple DES use in the form E(K1, Tran( E(K2, Tran( E(K3, Compress( x )))))), where each DES instance has its own key and IV (for CBC mode) and Tran is a large-block transposition program. Tran is available from [FTPTR]. This claims to gain security by diffusing single bit changes over a much larger block (Tran's block size). Other compositions of weak ciphers with DES are possible. For example, one could use: E(K1, Prngxor(K4, Tran( E(K2, Tran( Prngxor(K5, E(K3, Compress( x )))))))), where Prngxor() [FTPPX] is a simple stream cipher driven from a long-period pseudo-random number generator (PRNG), to make sure that all plaintext or ciphertext patterns are hidden while permitting the use of ECB mode for DES (since there are certain weaknesses in the use of inner CBC loops for multiple-DES, under some attacks, and we do not yet know if these show up under composition with Tran()). 5.9. What is differential cryptanalysis? Differential cryptanalysis is a statistical attack that can be applied to any iterated mapping (i.e., any mapping which is based on a repeated round function). The method was recently popularized by Biham and Shamir [BIH91], but Coppersmith has remarked that the S-boxes of DES were optimized against this attack some 20 years ago. This method has proved effective against several product ciphers, notably FEAL [BI91a]. Differential cryptanalysis is based on observing a large number of ciphertexts Y, Y' whose corresponding plaintexts X, X' satisfy a known difference D = X+X', where + is componentwise XOR. In the basic Biham-Shamir attack, 2^{47} such plaintext pairs are required to determine the key for DES. Substantially fewer pairs are required if DES is truncated to 6 or 8 rounds. In these cases, the actual key can be recovered in a matter of minutes using a few thousand pairs. For full DES this attack is impractical because it requires so many known plaintexts. The work of Biham and Shamir on DES revealed several startling observations on the algorithm. Most importantly, if the key schedule was removed from DES and a 16*48 = 768-bit key was used, the key could be recovered in less than 2^{64} steps. Thus independent subkeys do not add substantial security to DES. Further, the S-boxes of DES are extremely sensitive in that changing even single entries in these tables yields significant improvement in the differential attack. Adi Shamir is quoted to say (NYTimes Oct 13 1991), ``I would say that, contrary to what some people believe, there is no evidence of tampering with the DES so that the basic design was weakened.'' 5.10. How was NSA involved in the design of DES? According to Kinnucan [KIN78], Tuchman, a member of the group that developed DES at IBM is quoted as saying, ``We developed the DES algorithm entirely within IBM using IBMers. The NSA did not dictate a single wire!'' Tuchman and Meyer (another developer of DES) spent a year breaking ciphers and finding weaknesses in Lucifer. They then spent two years strengthening Lucifer. ``Their basic approach was to look for strong substitution, permutation, and key scheduling functions ... IBM has classified the notes containing the selection criteria at the request of the NSA.... `The NSA told us we had inadvertently reinvented some of the deep secrets it uses to make its own algorithms,' explains Tuchman.'' On the other hand, a document called ``Involvement of the NSA in the development of DES: unclassified summary of the United States Select Committee on Intelligence'', printed in the IEEE Communications Magazine, p53-55, 1978, states: ``In the development of DES, NSA convinced IBM that a reduced keysize was sufficient; indirectly assisted in the development of the S-box structures; and certified that the final DES algorithm was, to the best of their knowledge, free from any statistical or mathematical weakness.'' Clearly the key size was reduced at the insistence of the NSA. The article further states that the NSA did not tamper with the algorithm itself, just the parameters, which in some sense resolves the apparent conflict in the remarks of Meyer and Tuchman presented above. 5.11. Is DES available in software? Several people have made DES code available via ftp (see part 10 for pathnames): Stig Ostholm [FTPSO]; BSD [FTPBK]; Eric Young [FTPEY]; Dennis Furguson [FTPDF]; Mark Riordan [FTPMR]; Phil Karn [FTPPK]. A Pascal listing of DES is also given in Patterson [PAT87]. Antti Louko <alo@kampi.hut.fi> has written a version of DES with BigNum packages in [FTPAL]. FIPS 46-1 says ``The algorithm specified in this standard is to be implemented ... using hardware (not software) technology. ... Software implementations in general purpose computers are not in compliance with this standard.'' Despite this, software implementations abound, and are used by government agencies. 5.12. Is DES available in hardware? The following paragraphs are quoted from messages sent to the editors. We don't vouch for the quality or even existence of the products. Christian Franke, franke@informatik.rwth-aachen.de, says: ``1. Cryptech CRY12C102: 22.5Mbit/s according to Data Sheet, with 32 Bit interface. We use this one, because it was the only one available when we started the project. No problems ! 2. Pijnenburg PCC100: 20Mbit/s according to Data Sheet. Address: PIJNENBURG B.V., Boxtelswweg 26, NL-5261 NE Vught, The Netherlands. 3. INFOSYS DES Chip (Germany): S-Boxes must be loaded by software. So you can modify the Algorithm. Sorry, I don't have the data sheet handy. Please E-Mail me if you need further information.'' Marcus J Ranum, mjr@tis.com, says: ``SuperCrypt'' 100Mb/sec and faster DES and Proprietary Storage for 16 56-bit keys Key stream generator Integrated hardware DES3 procedure Extended mode with 112 bit keys; Computer Elektronik Infosys; 512-A Herndon Parkway,; Herndon, VA 22070; 800-322-3464. Tim Hember, thember@gandalf.ca, says: Newbridge Microsystems sells an AM9568 compatible DES chip that operates at 25MHz, performs a round of encryption in 18 clocks, has a three-stage pipeline, supports ECB, CBC, CFB-8 and >>> CFB-1 <<<<. Further it is very reasonable priced as opposed to other high-end DES chips. Call Newbridge Microsystems, Ottawa, 613-592-0714. (... there are no import/export issues with Canada and the US). If you require custom DES or Public Key ICs then Timestep Engineering developed Newbridge's crypto chips and ICs for other commercial and educational establishments. They can be reached at 613-820-0024. 5.13. Can DES be used to protect classified information? DES is not intended to protect classified data. FIPS 46-1 says: ``This standard will be used by Federal departments and agencies for the cryptographic protection of computer data when the following conditions apply: 1. ... cryptographic protection is required; and 2. the data is not classified according to the National Security Act of 1947, as amended, or the Atomic Energy Act of 1954, as amended.'' 5.14. What are ECB, CBC, CFB, OFB, and PCBC encryption? These are methods for using block ciphers, such as DES, to encrypt messages, files, and blocks of data, known as ``modes of operation.'' Four ``modes of operation'' are defined in FIPS 81 (1980 December 2), and also in ANSI X3.106-1983. FIPS 81 specifies that when 7-bit ASCII data is sent in octets, the unused most-significant bit is to be set to 1. FIPS 81 also specifies the padding for short blocks. The four FIPS/ANSI standard DES modes of operation are: Electronic Code Book (ECB), Cipher Block Chaining (CBC), K-bit Cipher FeedBack (CFB), and K-bit Output FeedBack (OFB). All four of the ANSI/FIPS modes have very little "error extension". For a single bit error in the cipherstream, none of them produce an error burst in the decrypted output stream of longer than 128 bits. A fifth mode of operation, used in Kerberos and elsewhere but not defined in any standard, is error-Propagating Cipher Block Chaining (PCBC). Unlike the 4 standard modes, PCBC extends or propagates the effect of a single bit error in the cipherstream throughout remainder of the decrypted textstream after the point of error. These 5 methods are explained below in a C-language-like notation. Some symbols: P[n] The n'th block of plaintext, input to encryption, output from decryption. Size of block determined by the mode. C[n] The n'th block of ciphertext, output from encryption, input to decryption. Size of block determined by the mode. E(m) The DES encryption function, performed on 64-bit block m, using the 16-key schedule derived from some 56-bit key. D(m) The DES decryption function, performed on 64-bit block m, using the same key schedule as in E(m), except that the 16 keys in the schedule are used in the opposite order as in E(m). IV A 64-bit ``initialization vector'', a secret value which, along with the key, is shared by both encryptor and decryptor. I[n] The n'th value of a 64-bit variable, used in some modes. R[n] The n'th value of a 64-bit variable, used in some modes. LSB(m,k) The k least significant (right-most) bits of m. e.g. m & ((1 << k) - 1) MSB(m,k) The k most significant (left-most) bits of m. e.g. (m >> (64-k)) & ((1 << k) - 1) = ^ << >> & operators as defined in the c langage. Electronic Code Book (ECB): P[n] and C[n] are each 64-bits long. Encryption: Decryption: C[n] = E(P[n]) P[n] = D(C[n]) Cipher Block Chaining (CBC): P[n] and C[n] are each 64-bits long. Encryption: Decryption: C[0] = E(P[0]^IV) P[0] = D(C[0])^IV (n>0) C[n] = E(P[n]^C[n-1]) P[n] = D(C[n])^C[n-1] Propagating Cipher Block Chaining (PCBC): P[n] and C[n] are each 64-bits long. Encryption: Decryption: C[0] = E(P[0]^IV) P[0] = D(C[0])^IV (n>0) C[n] = E(P[n]^P[n-1]^C[n-1]) P[n] = D(C[n])^P[n-1]^C[n-1] k-bit Cipher FeedBack (CFB): P[n] and C[n] are each k bits long, 1 <= k <= 64. Encryption: Decryption: I[0] = IV I[0] = IV (n>0) I[n] = I[n-1]<<k | C[n-1] I[n] = I[n-1]<<k | C[n-1] (all n) R[n] = MSB(E(I[n]),k) R[n] = MSB(E(I[n]),k) (all n) C[n] = P[n]^R[n] P[n] = C[n]^R[n] Note that for k==64, this reduces to: I[0] = IV I[0] = IV (n>0) I[n] = C[n-1] I[n] = C[n-1] (all n) R[n] = E(I[n]) R[n] = E(I[n]) (all n) C[n] = P[n]^R[n] P[n] = C[n]^R[n] CFB notes: Since I[n] depends only on the plain or cipher text from the previous operation, the E() function can be performed in parallel with the reception of the text with which it is used. k-bit Output FeedBack (OFB): P[n] and C[n] are each k bits long, 1 <= k <= 64. Encryption: Decryption: I[0] = IV I[0] = IV (n>0) I[n] = I[n-1]<<k | R[n-1] I[n] = I[n-1]<<k | R[n-1] (all n) R[n] = MSB(E(I[n]),k) R[n] = MSB(E(I[n]),k) (all n) C[n] = P[n]^R[n] P[n] = C[n]^R[n] Note that for k==64, this reduces to: I[0] = IV I[0] = IV (n>0) I[n] = R[n-1] I[n] = R[n-1] (all n) R[n] = E(I[n]) R[n] = E(I[n]) (all n) C[n] = P[n]^R[n] P[n] = C[n]^R[n] OFB notes: encryption and decryption are identical. Since I[n] is independent of P and C, the E() function can be performed in advance of the receipt of the plain/cipher text with which it is to be used. Additional notes on DES ``modes of operation'': ECB and CBC use E() to encrypt and D() to decrypt, but the feedback modes use E() to both encrypt and decrypt. This disproves the following erroneous claim: ``DES implementations which provide E() but not D() cannot be used for data confidentiality.'' This is the sixth of ten parts of the sci.crypt FAQ. The parts are mostly independent, but you should read the first part before the rest. We don't have the time to send out missing parts by mail, so don't ask. Notes such as ``[KAH67]'' refer to the reference list in the last part. The sections of this FAQ are available via anonymous FTP to rtfm.mit.edu as /pub/usenet/news.answers/cryptography-faq/part[xx]. The Cryptography FAQ is posted to the newsgroups sci.crypt, talk.politics.crypto, sci.answers, and news.answers every 21 days. Contents: 6.1. What is public-key cryptography? 6.2. How does public-key cryptography solve cryptography's Catch-22? 6.3. What is the role of the `trapdoor function' in public key schemes? 6.4. What is the role of the `session key' in public key schemes? 6.5. What's RSA? 6.6. Is RSA secure? 6.7. What's the difference between the RSA and Diffie-Hellman schemes? 6.8. What is `authentication' and the `key distribution problem'? 6.9. How fast can people factor numbers? 6.10. What about other public-key cryptosystems? 6.11. What is the `RSA Factoring Challenge?' 6.1. What is public-key cryptography? In a classic cryptosystem, we have encryption functions E_K and decryption functions D_K such that D_K(E_K(P)) = P for any plaintext P. In a public-key cryptosystem, E_K can be easily computed from some ``public key'' X which in turn is computed from K. X is published, so that anyone can encrypt messages. If decryption D_K cannot be easily computed from public key X without knowledge of private key K, but readily with knowledge of K, then only the person who generated K can decrypt messages. That's the essence of public-key cryptography, introduced by Diffie and Hellman in 1976. This document describes only the rudiments of public key cryptography. There is an extensive literature on security models for public-key cryptography, applications of public-key cryptography, other applications of the mathematical technology behind public-key cryptography, and so on; consult the references at the end for more refined and thorough presentations. 6.2. How does public-key cryptography solve cryptography's Catch-22? In a classic cryptosystem, if you want your friends to be able to send secret messages to you, you have to make sure nobody other than them sees the key K. In a public-key cryptosystem, you just publish X, and you don't have to worry about spies. Hence public key cryptography `solves' one of the most vexing problems of all prior cryptography: the necessity of establishing a secure channel for the exchange of the key. To establish a secure channel one uses cryptography, but private key cryptography requires a secure channel! In resolving the dilemma, public key cryptography has been considered by many to be a `revolutionary technology,' representing a breakthrough that makes routine communication encryption practical and potentially ubiquitous. 6.3. What is the role of the `trapdoor function' in public key schemes? Intrinsic to public key cryptography is a `trapdoor function' D_K with the properties that computation in one direction (encryption, E_K) is easy and in the other is virtually impossible (attack, determining P from encryption E_K(P) and public key X). Furthermore, it has the special property that the reversal of the computation (decryption, D_K) is again tractable if the private key K is known. 6.4. What is the role of the `session key' in public key schemes? In virtually all public key systems, the encryption and decryption times are very lengthy compared to other block-oriented algorithms such as DES for equivalent data sizes. Therefore in most implementations of public-key systems, a temporary, random `session key' of much smaller length than the message is generated for each message and alone encrypted by the public key algorithm. The message is actually encrypted using a faster private key algorithm with the session key. At the receiver side, the session key is decrypted using the public-key algorithms and the recovered `plaintext' key is used to decrypt the message. The session key approach blurs the distinction between `keys' and `messages' -- in the scheme, the message includes the key, and the key itself is treated as an encryptable `message'. Under this dual-encryption approach, the overall cryptographic strength is related to the security of either the public- and private-key algorithms. 6.5. What's RSA? RSA is a public-key cryptosystem defined by Rivest, Shamir, and Adleman. Here's a small example. See also [FTPDQ]. Plaintexts are positive integers up to 2^{512}. Keys are quadruples (p,q,e,d), with p a 256-bit prime number, q a 258-bit prime number, and d and e large numbers with (de - 1) divisible by (p-1)(q-1). We define E_K(P) = P^e mod pq, D_K(C) = C^d mod pq. All quantities are readily computed from classic and modern number theoretic algorithms (Euclid's algorithm for computing the greatest common divisor yields an algorithm for the former, and historically newly explored computational approaches to finding large `probable' primes, such as the Fermat test, provide the latter.) Now E_K is easily computed from the pair (pq,e)---but, as far as anyone knows, there is no easy way to compute D_K from the pair (pq,e). So whoever generates K can publish (pq,e). Anyone can send a secret message to him; he is the only one who can read the messages. 6.6. Is RSA secure? Nobody knows. An obvious attack on RSA is to factor pq into p and q. See below for comments on how fast state-of-the-art factorization algorithms run. Unfortunately nobody has the slightest idea how to prove that factorization---or any realistic problem at all, for that matter---is inherently slow. It is easy to formalize what we mean by ``RSA is/isn't strong''; but, as Hendrik W. Lenstra, Jr., says, ``Exact definitions appear to be necessary only when one wishes to prove that algorithms with certain properties do _not_ exist, and theoretical computer science is notoriously lacking in such negative results.'' Note that there may even be a `shortcut' to breaking RSA other than factoring. It is obviously sufficient but so far not provably necessary. That is, the security of the system depends on two critical assumptions: (1) factoring is required to break the system, and (2) factoring is `inherently computationally intractable', or, alternatively, `factoring is hard' and `any approach that can be used to break the system is at least as hard as factoring'. Historically even professional cryptographers have made mistakes in estimating and depending on the intractability of various computational problems for secure cryptographic properties. For example, a system called a `Knapsack cipher' was in vogue in the literature for years until it was demonstrated that the instances typically generated could be efficiently broken, and the whole area of research fell out of favor. 6.7. What's the difference between the RSA and Diffie-Hellman schemes? Diffie and Hellman proposed a system that requires the dynamic exchange of keys for every sender-receiver pair (and in practice, usually every communications session, hence the term `session key'). This two-way key negotiation is useful in further complicating attacks, but requires additional communications overhead. The RSA system reduces communications overhead with the ability to have static, unchanging keys for each receiver that are `advertised' by a formal `trusted authority' (the hierarchical model) or distributed in an informal `web of trust'. 6.8. What is `authentication' and the `key-exchange problem'? The ``key exchange problem'' involves (1) ensuring that keys are exchanged so that the sender and receiver can perform encryption and decryption, and (2) doing so in such a way that ensures an eavesdropper or outside party cannot break the code. `Authentication' adds the requirement that (3) there is some assurance to the receiver that a message was encrypted by `a given entity' and not `someone else'. The simplest but least available method to ensure all constraints above are satisfied (successful key exchange and valid authentication) is employed by private key cryptography: exchanging the key secretly. Note that under this scheme, the problem of authentication is implicitly resolved. The assumption under the scheme is that only the sender will have the key capable of encrypting sensible messages delivered to the receiver. While public-key cryptographic methods solve a critical aspect of the `key-exchange problem', specifically their resistance to analysis even with the presence a passive eavesdropper during exchange of keys, they do not solve all problems associated with key exchange. In particular, since the keys are considered `public knowledge,' (particularly with RSA) some other mechanism must be developed to testify to authenticity, because possession of keys alone (sufficient to encrypt intelligible messages) is no evidence of a particular unique identity of the sender. One solution is to develop a key distribution mechanism that assures that listed keys are actually those of the given entities, sometimes called a `trusted authority'. The authority typically does not actually generate keys, but does ensure via some mechanism that the lists of keys and associated identities kept and advertised for reference by senders and receivers are `correct'. Another method relies on users to distribute and track each other's keys and trust in an informal, distributed fashion. This has been popularized as a viable alternative by the PGP software which calls the model the `web of trust'. Under RSA, if a person wishes to send evidence of their identity in addition to an encrypted message, they simply encrypt some information with their private key called the `signature', additionally included in the message sent under the public-key encryption to the receiver. The receiver can use the RSA algorithm `in reverse' to verify that the information decrypts sensibly, such that only the given entity could have encrypted the plaintext by use of the secret key. Typically the encrypted `signature' is a `message digest' that comprises a unique mathematical `summary' of the secret message (if the signature were static across multiple messages, once known previous receivers could use it falsely). In this way, theoretically only the sender of the message could generate their valid signature for that message, thereby authenticating it for the receiver. `Digital signatures' have many other design properties as described in Section 7. 6.9. How fast can people factor numbers? It depends on the size of the numbers, and their form. Numbers in special forms, such as a^n - b for `small' b, are more readily factored through specialized techniques and not necessarily related to the difficulty of factoring in general. Hence a specific factoring `breakthrough' for a special number form may have no practical value or relevance to particular instances (and those generated for use in cryptographic systems are specifically `filtered' to resist such approaches.) The most important observation about factoring is that all known algorithms require an exponential amount of time in the _size_ of the number (measured in bits, log2(n) where `n' is the number). Cryptgraphic algorithms built on the difficulty of factoring generally depend on this exponential-time property. (The distinction of `exponential' vs. `polynomial time' algorithms, or NP vs. P, is a major area of active computational research, with insights very closely intertwined with cryptographic security.) In October 1992 Arjen Lenstra and Dan Bernstein factored 2^523 - 1 into primes, using about three weeks of MasPar time. (The MasPar is a 16384-processor SIMD machine; each processor can add about 200000 integers per second.) The algorithm there is called the ``number field sieve''; it is quite a bit faster for special numbers like 2^523 - 1 than for general numbers n, but it takes time only exp(O(log^{1/3} n log^{2/3} log n)) in any case. An older and more popular method for smaller numbers is the ``multiple polynomial quadratic sieve'', which takes time exp(O(log^{1/2} n log^{1/2} log n))---faster than the number field sieve for small n, but slower for large n. The breakeven point is somewhere between 100 and 150 digits, depending on the implementations. Factorization is a fast-moving field---the state of the art just a few years ago was nowhere near as good as it is now. If no new methods are developed, then 2048-bit RSA keys will always be safe from factorization, but one can't predict the future. (Before the number field sieve was found, many people conjectured that the quadratic sieve was asymptotically as fast as any factoring method could be.) 6.10. What about other public-key cryptosystems? We've talked about RSA because it's well known and easy to describe. But there are lots of other public-key systems around, many of which are faster than RSA or depend on problems more widely believed to be difficult. This has been just a brief introduction; if you really want to learn about the many facets of public-key cryptography, consult the books and journal articles listed in part 10. 6.11. What is the ``RSA Factoring Challenge''? [Note: The e-mail addresses below have been reported as invalid.] In ~1992 the RSA Data Securities Inc., owner and licensor of multiple patents on the RSA hardware and public key cryptographic techniques in general, and maker of various software encryption packages and libraries, announced on sci.math and elsewhere the creation of an ongoing Factoring Challenge contest to gauge the state of the art in factoring technology. Every month a series of numbers are posted and monetary awards are given to the first respondent to break them into factors. Very significant hardware resources are required to succeed by beating other participants. Information can be obtained via automated reply from challenge-rsa-honor-roll@rsa.com challenge-partition-honor-roll@rsa.com This is the seventh of ten parts of the sci.crypt FAQ. The parts are mostly independent, but you should read the first part before the rest. We don't have the time to send out missing parts by mail, so don't ask. Notes such as ``[KAH67]'' refer to the reference list in the last part. The sections of this FAQ are available via anonymous FTP to rtfm.mit.edu as /pub/usenet/news.answers/cryptography-faq/part[xx]. The Cryptography FAQ is posted to the newsgroups sci.crypt, talk.politics.crypto, sci.answers, and news.answers every 21 days. Contents: 7.1. What is a one-way hash function? 7.2. What is the difference between public, private, secret, shared, etc.? 7.3. What are MD4 and MD5? 7.4. What is Snefru? 7.1. What is a one-way hash function? A typical one-way hash function takes a variable-length message and produces a fixed-length hash. Given the hash it is computationally impossible to find a message with that hash; in fact one can't determine any usable information about a message with that hash, not even a single bit. For some one-way hash functions it's also computationally impossible to determine two messages which produce the same hash. A one-way hash function can be private or public, just like an encryption function. Here's one application of a public one-way hash function, like MD5 or Snefru. Most public-key signature systems are relatively slow. To sign a long message may take longer than the user is willing to wait. Solution: Compute the one-way hash of the message, and sign the hash, which is short. Now anyone who wants to verify the signature can do the same thing. Another name for one-way hash function is message digest function. 7.2. What is the difference between public, private, secret, shared, etc.? There is a horrendous mishmash of terminology in the literature for a very small set of concepts. Here are the concepts: (1) When an algorithm depends on a key which isn't published, we call it a private algorithm; otherwise we call it a public algorithm. (2) We have encryption functions E and decryption functions D, so that D(E(M)) = M for any message M. (3) We also have hashing functions H and verification functions V, such that V(M,X) = 1 if and only if X = H(M). A public-key cryptosystem has public encryption and private decryption. Checksums, such as the application mentioned in the previous question, have public hashing and public verification. Digital signature functions have private hashing and public verification: only one person can produce the hash for a message, but everyone can verify that the hash is correct. Obviously, when an algorithm depends on a private key, it's meant to be unusable by anyone who doesn't have the key. There's no real difference between a ``shared'' key and a private key: a shared key isn't published, so it's private. If you encrypt data for a friend rather than ``for your eyes only'', are you suddenly doing ``shared-key encryption'' rather than private-key encryption? No. 7.3. What are MD4 and MD5? MD4 and MD5 are message digest functions developed by Ron Rivest. Definitions appear in RFC 1320 and RFC 1321 (see part 10). Code is available from [FTPMD]. Note that a transcription error was found in the original MD5 draft RFC. The corrected algorithm should be called MD5a, though some people refer to it as MD5. 7.4. What is Snefru? Snefru is a family of message digest functions developed by Ralph Merkle. Snefru-8 is an 8-round function, the newest in the family. Definitions appear in Merkle's paper [ME91a]. Code is available from [FTPSF]. This is the eighth of ten parts of the sci.crypt FAQ. The parts are mostly independent, but you should read the first part before the rest. We don't have the time to send out missing parts by mail, so don't ask. Notes such as ``[KAH67]'' refer to the reference list in the last part. The sections of this FAQ are available via anonymous FTP to rtfm.mit.edu as /pub/usenet/news.answers/cryptography-faq/part[xx]. The Cryptography FAQ is posted to the newsgroups sci.crypt, talk.politics.crypto, sci.answers, and news.answers every 21 days. Contents 8.1. How do I recover from lost passwords in WordPerfect? 8.2. How do I break a Vigenere (repeated-key) cipher? 8.3. How do I send encrypted mail under UNIX? [PGP, RIPEM, PEM, ...] 8.4. Is the UNIX crypt command secure? 8.5. How do I use compression with encryption? 8.6. Is there an unbreakable cipher? 8.7. What does ``random'' mean in cryptography? 8.8. What is the unicity point (a.k.a. unicity distance)? 8.9. What is key management and why is it important? 8.10. Can I use pseudo-random or chaotic numbers as a key stream? 8.11. What is the correct frequency list for English letters? 8.12. What is the Enigma? 8.13. How do I shuffle cards? 8.14. Can I foil S/W pirates by encrypting my CD-ROM? 8.15. Can you do automatic cryptanalysis of simple ciphers? 8.16. What is the coding system used by VCR+? 8.1. How do I recover from lost passwords in WordPerfect? WordPerfect encryption has been shown to be very easy to break. The method uses XOR with two repeating key streams: a typed password and a byte-wide counter initialized to 1+<the password length>. Full descriptions are given in Bennett [BEN87] and Bergen and Caelli [BER91]. Chris Galas writes: ``Someone awhile back was looking for a way to decrypt WordPerfect document files and I think I have a solution. There is a software company named: Accessdata (87 East 600 South, Orem, UT 84058), 1-800-658-5199 that has a software package that will decrypt any WordPerfect, Lotus 1-2-3, Quatro-Pro, MS Excel and Paradox files. The cost of the package is $185. Steep prices, but if you think your pw key is less than 10 characters, (or 10 char) give them a call and ask for the free demo disk. The demo disk will decrypt files that have a 10 char or less pw key.'' Bruce Schneier says the phone number for AccessData is 801-224-6970. 8.2. How do I break a Vigenere (repeated-key) cipher? A repeated-key cipher, where the ciphertext is something like the plaintext xor KEYKEYKEYKEY (and so on), is called a Vigenere cipher. If the key is not too long and the plaintext is in English, do the following: 1. Discover the length of the key by counting coincidences. (See Gaines [GAI44], Sinkov [SIN66].) Trying each displacement of the ciphertext against itself, count those bytes which are equal. If the two ciphertext portions have used the same key, something over 6% of the bytes will be equal. If they have used different keys, then less than 0.4% will be equal (assuming random 8-bit bytes of key covering normal ASCII text). The smallest displacement which indicates an equal key is the length of the repeated key. 2. Shift the text by that length and XOR it with itself. This removes the key and leaves you with text XORed with itself. Since English has about 1 bit of real information per byte, 2 streams of text XORed together has 2 bits of info per 8-bit byte, providing plenty of redundancy for choosing a unique decryption. (And in fact one stream of text XORed with itself has just 1 bit per byte.) If the key is short, it might be even easier to treat this as a standard polyalphabetic substitution. All the old cryptanalysis texts show how to break those. It's possible with those methods, in the hands of an expert, if there's only ten times as much text as key. See, for example, Gaines [GAI44], Sinkov [SIN66]. 8.3. How do I send encrypted mail under UNIX? [PGP, RIPEM, PEM, ...] Here's one popular method, using the des command: cat file | compress | des private_key | uuencode | mail Meanwhile, there is a de jure Internet standard in the works called PEM (Privacy Enhanced Mail). It is described in RFCs 1421 through 1424. To join the PEM mailing list, contact pem-dev-request@tis.com. There is a beta version of PEM being tested at the time of this writing. There are also two programs available in the public domain for encrypting mail: PGP and RIPEM. Both are available by FTP. Each has its own newsgroup: alt.security.pgp and alt.security.ripem. Each has its own FAQ as well. PGP is most commonly used outside the USA since it uses the RSA algorithm without a license and RSA's patent is valid only (or at least primarily) in the USA. RIPEM is most commonly used inside the USA since it uses the RSAREF which is freely available within the USA but not available for shipment outside the USA. Since both programs use a secret key algorithm for encrypting the body of the message (PGP used IDEA; RIPEM uses DES) and RSA for encrypting the message key, they should be able to interoperate freely. Although there have been repeated calls for each to understand the other's formats and algorithm choices, no interoperation is available at this time (as far as we know). 8.4. Is the UNIX crypt command secure? No. See [REE84]. There is a program available called cbw (crypt breaker's workbench) which can be used to do ciphertext-only attacks on files encrypted with crypt. One source for CBW is [FTPCB]. 8.5. How do I use compression with encryption? A number of people have proposed doing perfect compression followed by some simple encryption method (e.g., XOR with a repeated key). This would work, if you could do perfect compression. Unfortunately, you can only compress perfectly if you know the exact distribution of possible inputs, and that is almost certainly not possible. Compression aids encryption by reducing the redundancy of the plaintext. This increases the amount of ciphertext you can send encrypted under a given number of key bits. (See "unicity distance") Nearly all practical compression schemes, unless they have been designed with cryptography in mind, produce output that actually starts off with high redundancy. For example, the output of UNIX compress begins with a well-known three-byte ``magic number''. This produces a field of "known plaintext" which can be used for some forms of cryptanalytic attack. Compression is generally of value, however, because it removes other known plaintext in the middle of the file being encrypted. In general, the lower the redundancy of the plaintext being fed an encryption algorithm, the more difficult the cryptanalysis of that algorithm. In addition, compression shortens the input file, shortening the output file and reducing the amount of CPU required to do the encryption algorithm, so even if there were no enhancement of security, compression before encryption would be worthwhile. Compression after encryption is silly. If an encryption algorithm is good, it will produce output which is statistically indistinguishable from random numbers and no compression algorithm will successfully compress random numbers. On the other hand, if a compression algorithm succeeds in finding a pattern to compress out of an encryption's output, then a flaw in that algorithm has been found. 8.6. Is there an unbreakable cipher? Yes. The one-time pad is unbreakable; see part 4. Unfortunately the one-time pad requires secure distribution of as much key material as plaintext. Of course, a cryptosystem need not be utterly unbreakable to be useful. Rather, it needs to be strong enough to resist attacks by likely enemies for whatever length of time the data it protects is expected to remain valid. 8.7. What does ``random'' mean in cryptography? Cryptographic applications demand much more out of a pseudorandom number generator than most applications. For a source of bits to be cryptographically random, it must be computationally impossible to predict what the Nth random bit will be given complete knowledge of the algorithm or hardware generating the stream and the sequence of 0th through N-1st bits, for all N up to the lifetime of the source. A software generator (also known as pseudo-random) has the function of expanding a truly random seed to a longer string of apparently random bits. This seed must be large enough not to be guessed by the opponent. Ideally, it should also be truly random (perhaps generated by a hardware random number source). Those who have Sparcstation 1 workstations could, for example, generate random numbers using the audio input device as a source of entropy, by not connecting anything to it. For example, cat /dev/audio | compress - >foo gives a file of high entropy (not random but with much randomness in it). One can then encrypt that file using part of itself as a key, for example, to convert that seed entropy into a pseudo-random string. When looking for hardware devices to provide this entropy, it is important really to measure the entropy rather than just assume that because it looks complicated to a human, it must be "random". For example, disk operation completion times sound like they might be unpredictable (to many people) but a spinning disk is much like a clock and its output completion times are relatively low in entropy. 8.8. What is the unicity point (a.k.a. unicity distance)? See [SHA49]. The unicity distance is an approximation to that amount of ciphertext such that the sum of the real information (entropy) in the corresponding source text and encryption key equals the number of ciphertext bits used. Ciphertexts significantly longer than this can be shown probably to have a unique decipherment. This is used to back up a claim of the validity of a ciphertext-only cryptanalysis. Ciphertexts significantly shorter than this are likely to have multiple, equally valid decryptions and therefore to gain security from the opponent's difficulty choosing the correct one. Unicity distance, like all statistical or information-theoretic measures, does not make deterministic predictions but rather gives probabilistic results: namely, the minimum amount of ciphertext for which it is likely that there is only a single intelligible plaintext corresponding to the ciphertext, when all possible keys are tried for the decryption. Working cryptologists don't normally deal with unicity distance as such. Instead they directly determine the likelihood of events of interest. Let the unicity distance of a cipher be D characters. If fewer than D ciphertext characters have been intercepted, then there is not enough information to distinguish the real key from a set of possible keys. DES has a unicity distance of 17.5 characters, which is less than 3 ciphertext blocks (each block corresponds to 8 ASCII characters). This may seem alarmingly low at first, but the unicity distance gives no indication of the computational work required to find the key after approximately D characters have been intercepted. In fact, actual cryptanalysis seldom proceeds along the lines used in discussing unicity distance. (Like other measures such as key size, unicity distance is something that guarantees insecurity if it's too small, but doesn't guarantee security if it's high.) Few practical cryptosystems are absolutely impervious to analysis; all manner of characteristics might serve as entering ``wedges'' to crack some cipher messages. However, similar information-theoretic considerations are occasionally useful, for example, to determine a recommended key change interval for a particular cryptosystem. Cryptanalysts also employ a variety of statistical and information-theoretic tests to help guide the analysis in the most promising directions. Unfortunately, most literature on the application of information statistics to cryptanalysis remains classified, even the seminal 1940 work of Alan Turing (see [KOZ84]). For some insight into the possibilities, see [KUL68] and [GOO83]. 8.9. What is key management and why is it important? One of the fundamental axioms of cryptography is that the enemy is in full possession of the details of the general cryptographic system, and lacks only the specific key data employed in the encryption. (Of course, one would assume that the CIA does not make a habit of telling Mossad about its cryptosystems, but Mossad probably finds out anyway.) Repeated use of a finite amount of key provides redundancy that can eventually facilitate cryptanalytic progress. Thus, especially in modern communication systems where vast amounts of information are transferred, both parties must have not only a sound cryptosystem but also enough key material to cover the traffic. Key management refers to the distribution, authentication, and handling of keys. A publicly accessible example of modern key management technology is the STU III secure telephone unit, which for classified use employs individual coded ``Crypto Ignition Keys'' and a central Key Management Center operated by NSA. There is a hierarchy in that certain CIKs are used by authorized cryptographic control personnel to validate the issuance of individual traffic keys and to perform installation/maintenance functions, such as the reporting of lost CIKs. This should give an inkling of the extent of the key management problem. For public-key systems, there are several related issues, many having to do with ``whom do you trust?'' 8.10. Can I use pseudo-random or chaotic numbers as a key stream? Chaotic equations and fractals produce an apparent randomness from relatively compact generators. Perhaps the simplest example is a linear congruential sequence, one of the most popular types of random number generators, where there is no obvious dependence between seeds and outputs. Unfortunately the graph of any such sequence will, in a high enough dimension, show up as a regular lattice. Mathematically this lattice corresponds to structure which is notoriously easy for cryptanalysts to exploit. More complicated generators have more complicated structure, which is why they make interesting pictures--- but a cryptographically strong sequence will have no computable structure at all. See [KNU81], exercise 3.5-7; [REE77]; and [BOY89]. 8.11. What is the correct frequency list for English letters? There are three answers to this question, each slightly deeper than the one before. You can find the first answer in various books: namely, a frequency list computed directly from a certain sample of English text. The second answer is that ``the English language'' varies from author to author and has changed over time, so there is no definitive list. Of course the lists in the books are ``correctly'' computed, but they're all different: exactly which list you get depends on which sample was taken. Any particular message will have different statistics from those of the language as a whole. The third answer is that yes, no particular message is going to have exactly the same characteristics as English in general, but for all reasonable statistical uses these slight discrepancies won't matter. In fact there's an entire field called ``Bayesian statistics'' (other buzzwords are ``maximum entropy methods'' and ``maximum likelihood estimation'') which studies questions like ``What's the chance that a text with these letter frequencies is in English?'' and comes up with reasonably robust answers. So make your own list from your own samples of English text. It will be good enough for practical work, if you use it properly. 8.12. What is the Enigma? ``For a project in data security we are looking for sources of information about the German Enigma code and how it was broken by the British during WWII.'' See [WEL82], [DEA85], [KOZ84], [HOD83], [KAH91]. 8.13. How do I shuffle cards? Card shuffling is a special case of the permutation of an array of values, using a random or pseudo-random function. All possible output permutations of this process should be equally likely. To do this, you need a random function (modran(x)) which will produce a uniformly distributed random integer in the interval [0..x-1]. Given that function, you can shuffle with the following [C] code: (assuming ARRLTH is the length of array arr[] and swap() interchanges values at the two addresses given) for ( n = ARRLTH-1; n > 0 ; n-- ) swap( &arr[modran( n+1 )], &arr[n] ) ; modran(x) can not be achieved exactly with a simple (ranno() % x) since ranno()'s interval may not be divisible by x, although in most cases the error will be very small. To cover this case, one can take ranno()'s modulus mod x, call that number y, and if ranno() returns a value less than y, go back and get another ranno() value. See [KNU81] for further discussion. 8.14. Can I foil S/W pirates by encrypting my CD-ROM? Someone will frequently express the desire to publish a CD-ROM with possibly multiple pieces of software, perhaps with each encrypted separately, and will want to use different keys for each user (perhaps even good for only a limited period of time) in order to avoid piracy. As far as we know, this is impossible, since there is nothing in standard PC or workstation hardware which uniquely identifies the user at the keyboard. If there were such an identification, then the CD-ROM could be encrypted with a key based in part on the one sold to the user and in part on the unique identifier. However, in this case the CD-ROM is one of a kind and that defeats the intended purpose. If the CD-ROM is to be encrypted once and then mass produced, there must be a key (or set of keys) for that encryption produced at some stage in the process. That key is useable with any copy of the CD-ROM's data. The pirate needs only to isolate that key and sell it along with the illegal copy. 8.15. Can you do automatic cryptanalysis of simple ciphers? Certainly. For commercial products you can try AccessData; see question 8.1. We are not aware of any FTP sites for such software, but there are many papers on the subject. See [PEL79], [LUC88], [CAR86], [CAR87], [KOC87], [KOC88], [KIN92], [KIN93], [SPI93]. 8.16. What is the coding system used by VCR+? One very frequently asked question in sci.crypt is how the VCR+ codes work. The codes are used to program a VCR based on numerical input. See [SHI92] for an attempt to describe it. This is the ninth of ten parts of the sci.crypt FAQ. The parts are mostly independent, but you should read the first part before the rest. We don't have the time to send out missing parts by mail, so don't ask. Notes such as ``[KAH67]'' refer to the reference list in the last part. The sections of this FAQ are available via anonymous FTP to rtfm.mit.edu as /pub/usenet/news.answers/cryptography-faq/part[xx]. The Cryptography FAQ is posted to the newsgroups sci.crypt, talk.politics.crypto, sci.answers, and news.answers every 21 days. Contents: 9.1. What is the National Security Agency (NSA)? 9.2. What are the US export regulations? 9.3. What is TEMPEST? 9.4. What are the Beale Ciphers, and are they a hoax? 9.5. What is the American Cryptogram Association, and how do I get in touch? 9.6. Is RSA patented? 9.7. What about the Voynich manuscript? 9.1. What is the National Security Agency (NSA)? The NSA is the official communications security body of the U.S. government. It was given its charter by President Truman in the early 50's, and has continued research in cryptology till the present. The NSA is known to be the largest employer of mathematicians in the world, and is also the largest purchaser of computer hardware in the world. Governments in general have always been prime employers of cryptologists. The NSA probably possesses cryptographic expertise many years ahead of the public state of the art, and can undoubtedly break many of the systems used in practice; but for reasons of national security almost all information about the NSA is classified. Bamford's book [BAMFD] gives a history of the people and operations of the NSA. The following quote from Massey [MAS88] highlights the difference between public and private research in cryptography: ``... if one regards cryptology as the prerogative of government, one accepts that most cryptologic research will be conducted behind closed doors. Without doubt, the number of workers engaged today in such secret research in cryptology far exceeds that of those engaged in open research in cryptology. For only about 10 years has there in fact been widespread open research in cryptology. There have been, and will continue to be, conflicts between these two research communities. Open research is common quest for knowledge that depends for its vitality on the open exchange of ideas via conference presentations and publications in scholarly journals. But can a government agency, charged with responsibilities of breaking the ciphers of other nations, countenance the publication of a cipher that it cannot break? Can a researcher in good conscience publish such a cipher that might undermine the effectiveness of his own government's code-breakers? One might argue that publication of a provably-secure cipher would force all governments to behave like Stimson's `gentlemen', but one must be aware that open research in cryptography is fraught with political and ethical considerations of a severity than in most scientific fields. The wonder is not that some conflicts have occurred between government agencies and open researchers in cryptology, but rather that these conflicts (at least those of which we are aware) have been so few and so mild.'' 9.2. What are the US export regulations? In a nutshell, there are two government agencies which control export of encryption software. One is the Bureau of Export Administration (BXA) in the Department of Commerce, authorized by the Export Administration Regulations (EAR). Another is the Office of Defense Trade Controls (DTC) in the State Department, authorized by the International Traffic in Arms Regulations (ITAR). As a rule of thumb, BXA (which works with COCOM) has less stringent requirements, but DTC (which takes orders from NSA) wants to see everything first and can refuse to transfer jurisdiction to BXA. The newsgroup misc.legal.computing carries many interesting discussions on the laws surrounding cryptographic export, what people think about those laws, and many other complex issues which go beyond the scope of technical groups like sci.crypt. Make sure to consult your lawyer before doing anything which will get you thrown in jail; if you are lucky, your lawyer might know a lawyer who has at least heard of the ITAR. 9.3. What is TEMPEST? TEMPEST is a standard for electromagnetic shielding for computer equipment. It was created in response to the discovery that information can be read from computer radiation (e.g., from a CRT) at quite a distance and with little effort. Needless to say, encryption doesn't do much good if the cleartext is available this way. 9.4. What are the Beale Ciphers, and are they a hoax? (Thanks to Jim Gillogly for this information and John King for corrections.) The story in a pamphlet by J. B. Ward (1885) goes: Thomas Jefferson Beale and a party of adventurers accumulated a huge mass of treasure and buried it in Bedford County, Virginia, leaving three ciphers with an innkeeper; the ciphers describe the location, contents, and intended beneficiaries of the treasure. Ward gives a decryption of the second cipher (contents) called B2; it was encrypted as a book cipher using the initial letters of the Declaration of Independence (DOI) as key. B1 and B3 are unsolved; many documents have been tried as the key to B1. Aficionados can join a group that attempts to solve B1 by various means with an eye toward splitting the treasure: The Beale Cypher Association P.O. Box 975 Beaver Falls, PA 15010 You can get the ciphers from the rec.puzzles FAQL by including the line: send index in a message to netlib@peregrine.com and following the directions. (There are apparently several different versions of the cipher floating around. The correct version is based on the 1885 pamphlet, says John King <kingj@hpcc01.corp.hp.com>.) Some believe the story is a hoax. Kruh [KRU88] gives a long list of problems with the story. Gillogly [GIL80] decrypted B1 with the DOI and found some unexpected strings, including ABFDEFGHIIJKLMMNOHPP. Hammer (president of the Beale Cypher Association) agrees that this string couldn't appear by chance, but feels there must be an explanation; Gwyn (sci.crypt expert) is unimpressed with this string. 9.5. What is the American Cryptogram Association, and how do I get in touch? The ACA is an organization devoted to cryptography, with an emphasis on cryptanalysis of systems that can be attacked either with pencil-and-paper or computers. Its organ ``The Cryptogram'' includes articles and challenge ciphers. Among the more than 50 cipher types in English and other languages are simple substitution, Playfair, Vigenere, bifid, Bazeries, grille, homophonic, and cryptarithm. Dues are $20 per year (6 issues) for new members, $15 thereafter; more outside North America; less for students under 18 and seniors. Send checks to ACA Treasurer, P.O. Box 198, Vernon Hills, IL 60061-0198. 9.6. Is RSA patented? Yes. The patent number is 4,405,829, filed 12/14/77, granted 9/20/83. For further discussion of this patent, whether it should have been granted, algorithm patents in general, and related legal and moral issues, see comp.patents and misc.legal.computing. For information about the League for Programming Freedom see [FTPPF]. Note that one of the original purposes of comp.patents was to collect questions such as ``should RSA be patented?'', which often flooded sci.crypt and other technical newsgroups, into a more appropriate forum. 9.7. What about the Voynich manuscript? The Voynich manuscript is an elaborately lettered and illustrated document, in a script never deciphered. It has been handed down for centuries by a line of art collectors and has uncertain origination. Much speculation and attention has been focused on its potential meaning. nelson@reed.edu (Nelson Minar) says there is a mailing list on the subject. The address to write to subscribe to the VMS mailing list is: <voynich-request@rand.org> the ftp archive is: rand.org:/pub/voynich There's all sorts of information about the manuscript itself, of course. A good bibliography can be found on the ftp site. [KAH67] gives a good introduction. This is the tenth of ten parts of the sci.crypt FAQ. The parts are mostly independent, but you should read the first part before the rest. We don't have the time to send out missing parts by mail, so don't ask. Notes such as ``[KAH67]'' refer to the reference list in this part. The sections of this FAQ are available via anonymous FTP to rtfm.mit.edu as /pub/usenet/news.answers/cryptography-faq/part[xx]. The Cryptography FAQ is posted to the newsgroups sci.crypt, talk.politics.crypto, sci.answers, and news.answers every 21 days. Contents 10.1. Books on history and classical methods 10.2. Books on modern methods 10.3. Survey articles 10.4. Reference articles 10.5. Journals, conference proceedings 10.6. Other 10.7. How may one obtain copies of FIPS and ANSI standards cited herein? 10.8. Electronic sources 10.9. RFCs (available from [FTPRF]) 10.10. Related newsgroups 10.1. Books on history and classical methods [FRIE1] Lambros D. Callimahos, William F. Friedman, Military Cryptanalytics. Aegean Park Press, ?. [DEA85] Cipher A. Deavours & Louis Kruh, Machine Cryptography and Modern Cryptanalysis. Artech House, 610 Washington St., Dedham, MA 02026, 1985. [FRIE2] William F. Friedman, Solving German Codes in World War I. Aegean Park Press, ?. [GAI44] H. Gaines, Cryptanalysis, a study of ciphers and their solution. Dover Publications, 1944. [HIN00] F.H.Hinsley, et al., British Intelligence in the Second World War. Cambridge University Press. (vol's 1, 2, 3a, 3b & 4, so far). XXX Years and authors, fix XXX [HOD83] Andrew Hodges, Alan Turing: The Enigma. Burnett Books Ltd., 1983 [KAH91] David Kahn, Seizing the Enigma. Houghton Mifflin, 1991. [KAH67] D. Kahn, The Codebreakers. Macmillan Publishing, 1967. [history] [The abridged paperback edition left out most technical details; the original hardcover edition is recommended.] [KOZ84] W. Kozaczuk, Enigma. University Publications of America, 1984 [KUL76] S. Kullback, Statistical Methods in Cryptanalysis. Aegean Park Press, 1976. [SIN66] A. Sinkov, Elementary Cryptanalysis. Math. Assoc. Am. 1966. [WEL82] Gordon Welchman, The Hut Six Story. McGraw-Hill, 1982. [YARDL] Herbert O. Yardley, The American Black Chamber. Aegean Park Press, ?. 10.2. Books on modern methods [BEK82] H. Beker, F. Piper, Cipher Systems. Wiley, 1982. [BRA88] G. Brassard, Modern Cryptology: a tutorial. Spinger-Verlag, 1988. [DEN82] D. Denning, Cryptography and Data Security. Addison-Wesley Publishing Company, 1982. [KOB89] N. Koblitz, A course in number theory and cryptography. Springer-Verlag, 1987. [KON81] A. Konheim, Cryptography: a primer. Wiley, 1981. [MEY82] C. Meyer and S. Matyas, Cryptography: A new dimension in computer security. Wiley, 1982. [PAT87] Wayne Patterson, Mathematical Cryptology for Computer Scientists and Mathematicians. Rowman & Littlefield, 1987. [PFL89] C. Pfleeger, Security in Computing. Prentice-Hall, 1989. [PRI84] W. Price, D. Davies, Security for computer networks. Wiley, 1984. [RUE86] R. Rueppel, Design and Analysis of Stream Ciphers. Springer-Verlag, 1986. [SAL90] A. Saloma, Public-key cryptography. Springer-Verlag, 1990. [SCH94] B. Schneier, Applied Cryptography. John Wiley & Sons, 1994. [errata avbl from schneier@chinet.com] [WEL88] D. Welsh, Codes and Cryptography. Claredon Press, 1988. 10.3. Survey articles [ANG83] D. Angluin, D. Lichtenstein, Provable Security in Crypto- systems: a survey. Yale University, Department of Computer Science, #288, 1983. [BET90] T. Beth, Algorithm engineering for public key algorithms. IEEE Selected Areas of Communication, 1(4), 458--466, 1990. [DAV83] M. Davio, J. Goethals, Elements of cryptology. in Secure Digital Communications, G. Longo ed., 1--57, 1983. [DIF79] W. Diffie, M. Hellman, Privacy and Authentication: An introduction to cryptography. IEEE proceedings, 67(3), 397--427, 1979. [DIF88] W. Diffie, The first ten years of public key cryptography. IEEE proceedings, 76(5), 560--577, 1988. [FEI73] H. Feistel, Cryptography and Computer Privacy. Scientific American, 228(5), 15--23, 1973. [FEI75] H. Feistel, H, W. Notz, J. Lynn Smith. Some cryptographic techniques for machine-to-machine data communications, IEEE IEEE proceedings, 63(11), 1545--1554, 1975. [HEL79] M. Hellman, The mathematics of public key cryptography. Scientific American, 130--139, 1979. [LAK83] S. Lakshmivarahan, Algorithms for public key cryptosystems. In Advances in Computers, M. Yovtis ed., 22, Academic Press, 45--108, 1983. [LEM79] A. Lempel, Cryptology in transition, Computing Surveys, 11(4), 285--304, 1979. [MAS88] J. Massey, An introduction to contemporary cryptology, IEEE proceedings, 76(5), 533--549, 1988. [SIM91] G. Simmons (ed.), Contemporary Cryptology: the Science of Information Integrity. IEEE press, 1991. 10.4. Reference articles [AND83] D. Andelman, J. Reeds, On the cryptanalysis of rotor and substitution-permutation networks. IEEE Trans. on Inform. Theory, 28(4), 578--584, 1982. [BEN87] John Bennett, Analysis of the Encryption Algorithm Used in the WordPerfect Word Processing Program. Cryptologia 11(4), 206--210, 1987. [BER91] H. A. Bergen and W. J. Caelli, File Security in WordPerfect 5.0. Cryptologia 15(1), 57--66, January 1991. [BIH91] E. Biham and A. Shamir, Differential cryptanalysis of DES-like cryptosystems. Journal of Cryptology, vol. 4, #1, 3--72, 1991. [BI91a] E. Biham, A. Shamir, Differential cryptanalysis of Snefru, Khafre, REDOC-II, LOKI and LUCIFER. In Proceedings of CRYPTO '91, ed. by J. Feigenbaum, 156--171, 1992. [BOY89] J. Boyar, Inferring Sequences Produced by Pseudo-Random Number Generators. Journal of the ACM, 1989. [BRI86] E. Brickell, J. Moore, M. Purtill, Structure in the S-boxes of DES. In Proceedings of CRYPTO '86, A. M. Odlyzko ed., 3--8, 1987. [BRO89] L. Brown, A proposed design for an extended DES, Computer Security in the Computer Age. Elsevier Science Publishers B.V. (North Holland), IFIP, W. J. Caelli ed., 9--22, 1989. [BRO90] L. Brown, J. Pieprzyk, J. Seberry, LOKI - a cryptographic primitive for authentication and secrecy applications. In Proceedings of AUSTCRYPT 90, 229--236, 1990. [CAE90] H. Gustafson, E. Dawson, W. Caelli, Comparison of block ciphers. In Proceedings of AUSCRYPT '90, J. Seberry and J. Piepryzk eds., 208--220, 1990. [CAM93] K. W. Campbell, M. J. Wiener, Proof the DES is Not a Group. In Proceedings of CRYPTO '92, 1993. [CAR86] John Carrol and Steve Martin, The Automated Cryptanalysis of Substitution Ciphers. Cryptologia 10(4), 193--209, 1986. [CAR87] John Carrol and Lynda Robbins, Automated Cryptanalysis of Polyalphabetic Ciphers. Cryptologia 11(4), 193--205, 1987. [ELL88] Carl M. Ellison, A Solution of the Hebern Messages. Cryptologia, vol. XII, #3, 144-158, Jul 1988. [EVE83] S. Even, O. Goldreich, DES-like functions can generate the alternating group. IEEE Trans. on Inform. Theory, vol. 29, #6, 863--865, 1983. [GAR91] G. Garon, R. Outerbridge, DES watch: an examination of the sufficiency of the Data Encryption Standard for financial institutions in the 1990's. Cryptologia, vol. XV, #3, 177--193, 1991. [GIL80] Gillogly, ?. Cryptologia 4(2), 1980. [GM82] Shafi Goldwasser, Silvio Micali, Probabilistic Encryption and How To Play Mental Poker Keeping Secret All Partial Information. Proceedings of the Fourteenth Annual ACM Symposium on Theory of Computing, 1982. [HUM83] D. G. N. Hunter and A. R. McKenzie, Experiments with Relaxation Algorithms for Breaking Simple Substitution Ciphers. Computer Journal 26(1), 1983. [KAM78] J. Kam, G. Davida, A structured design of substitution- permutation encryption networks. IEEE Trans. Information Theory, 28(10), 747--753, 1978. [KIN78] P. Kinnucan, Data encryption gurus: Tuchman and Meyer. Cryptologia, vol. II #4, 371--XXX, 1978. [KIN92] King and Bahler, Probabilistic Relaxation in the Cryptanalysis of Simple Substitution Ciphers. Cryptologia 16(3), 215--225, 1992. [KIN93] King and Bahler, An Algorithmic Solution of Sequential Homophonic Ciphers. Cryptologia 17(2), in press. [KOC87] Martin Kochanski, A Survey of Data Insecurity Packages. Cryptologia 11(1), 1--15, 1987. [KOC88] Martin Kochanski, Another Data Insecurity Package. Cryptologia 12(3), 165--177, 1988. [KRU88] Kruh, ?. Cryptologia 12(4), 1988. [LAI90] X. Lai, J. Massey, A proposal for a new block encryption standard. EUROCRYPT 90, 389--404, 1990. [LUB88] C. Rackoff, M. Luby, How to construct psuedorandom permutations from psuedorandom functions. SIAM Journal of Computing, vol. 17, #2, 373--386, 1988. [LUC88] Michael Lucks, A Constraint Satisfaction Algorithm for the Automated Decryption of Simple Substitution Ciphers. In CRYPTO '88. [MAS88] J. Massey, An introduction to contemporary cryptology. IEEE proceedings, 76(5), 533--549, 1988. [ME91a] R. Merkle, Fast software encryption functions. In Proceedings of CRYPTO '90, Menezes and Vanstone ed., 476--501, 1991. [MEY78] C. Meyer, Ciphertext/plaintext and ciphertext/key dependence vs. number of rounds for the Data Encryption Standard. AFIPS Conference proceedings, 47, 1119--1126, 1978. [NBS77] Data Encryption Standard. National Bureau of Standards, FIPS PUB 46, Washington, DC, January 1977. [PEL79] S. Peleg and A. Rosenfeld, Breaking Substitution Ciphers Using a Relaxation Algorithm. CACM 22(11), 598--605, 1979. [REE77] J. Reeds, `Cracking' a Random Number Generator. Cryptologia 1(1), 20--26, 1977. [REE84] J. A. Reeds and P. J. Weinberger, File Security and the UNIX Crypt Command. AT&T Bell Laboratories Technical Journal, Vol. 63 #8, part 2, 1673--1684, October, 1984. [SHA49] C. Shannon, Communication Theory of Secrecy Systems. Bell System Technical Journal 28(4), 656--715, 1949. [SHE88] B. Kaliski, R. Rivest, A. Sherman, Is the Data Encryption Standard a Group. Journal of Cryptology, vol. 1, #1, 1--36, 1988. [SHI88] A. Shimizu, S. Miyaguchi, Fast data encipherment algorithm FEAL. EUROCRYPT '87, 267--278, 1988. [SHI92] K. Shirriff, C. Welch, A. Kinsman, Decoding a VCR Controller Code. Cryptologia 16(3), 227--234, 1992. [SOR84] A. Sorkin, LUCIFER: a cryptographic algorithm. Cryptologia, 8(1), 22--35, 1984. [SPI93] R. Spillman et al., Use of Genetic Algorithms in Cryptanalysis of Simple Substitution Ciphers. Cryptologia 17(1), 31--44, 1993. 10.5. Journals, conference proceedings CRYPTO Eurocrypt IEEE Transactions on Information Theory Cryptologia: a cryptology journal, quarterly since Jan 1977. Cryptologia; Rose-Hulman Institute of Technology; Terre Haute Indiana 47803 [general: systems, analysis, history, ...] Journal of Cryptology; International Association for Cryptologic Research; published by Springer Verlag (quarterly since 1988). The Cryptogram (Journal of the American Cryptogram Association); 18789 West Hickory Street; Mundelein, IL 60060; [primarily puzzle cryptograms of various sorts] Cryptosystems Journal, Published by Tony Patti, P.O. Box 188, Newtown PA, USA 18940-0188 or tony_s_patti@cup.portal.com. Publisher's comment: Includes complete cryptosystems with source and executable programs on diskettes. Tutorial. The typical cryptosystems supports multi-megabit keys and Galois Field arithmetic. Inexpensive hardware random number generator details. Computer and Communication Security Reviews, published by Ross Anderson. Sample issue available from various ftp sites, including black.ox.ac.uk. Editorial c/o rja14@cl.cam.ac.uk. Publisher's comment: We review all the conference proceedings in this field, including not just Crypto and Eurocrypt, but regional gatherings like Auscrypt and Chinacrypt. We also abstract over 50 journals, and cover computer security as well as cryptology, so readers can see the research trends in applications as well as theory. Infosecurity News, MIS Training Institute Press, Inc. 498 Concord Street Framingham MA 01701-2357. This trade journal is oriented toward administrators and covers viruses, physical security, hackers, and so on more than cryptology. Furthermore, most of the articles are written by vendors and hence are biased. Nevertheless, there are occasionally some rather good cryptography articles. 10.6. Other Address of note: Aegean Park Press, P.O. Box 2837, Laguna Hills, CA 92654-0837. Answering machine at 714-586-8811. Toll Free at 800 736- 3587, and FAX at 714 586-8269. The ``Orange Book'' is DOD 5200.28-STD, published December 1985 as part of the ``rainbow book'' series. Write to Department of Defense, National Security Agency, ATTN: S332, 9800 Savage Road, Fort Meade, MD 20755-6000, and ask for the Trusted Computer System Evaluation Criteria. Or call 301-766-8729. The ``Orange Book'' will eventually be replaced by the U.S. Federal Criteria for Information Technology Security (FC) online at the NIST site [FTPNS], which also contains information on other various proposed and active federal standards. [BAMFD] Bamford, The Puzzle Palace. Penguin Books, 1982. [GOO83] I. J. Good, Good Thinking: the foundations of probability and its applications. University of Minnesota Press, 1983. [KNU81] D. E. Knuth, The Art of Computer Programming, volume 2: Seminumerical Algorithms. Addison-Wesley, 1981. [KUL68] Soloman Kullback, Information Theory and Statistics. Dover, 1968. [YAO88] A. Yao, Computational Information Theory. In Complexity in Information Theory, ed. by Abu-Mostafa, 1988. 10.7. How may one obtain copies of FIPS and ANSI standards cited herein? Many textbooks on cryptography contain complete reprints of the FIPS standards, which are not copyrighted. The following standards may be ordered from the U.S. Department of Commerce, National Technical Information Service, Springfield, VA 22161. FIPS PUB 46-1 Data Encryption Standard (this is DES) FIPS PUB 74 Guidelines for Implementing as Using the NBS DES FIPS PUB 81 DES Modes of Operation FIPS PUB 113 Computer Data Authentication (using DES) [Note: The address below has been reported as invalid.] The following standards may be ordered from the American National Standards Institute Sales Office, 1430 Broadway, New York, NY 10018. Phone 212.642.4900 ANSI X3.92-1981 Data Encryption Algorithm (identical to FIPS 46-1) ANSI X3.106-1983 DEA Modes of Operation (identical to FIPS 113) Notes: Figure 3 in FIPS PUB 46-1 is in error, but figure 3 in X3.92-1981 is correct. The text is correct in both publications. 10.8. Electronic sources Anonymous ftp: [FTPAL] kampi.hut.fi:alo/des-dist.tar.Z [FTPBK] ftp.uu.net:bsd-sources/usr.bin/des/ [FTPCB] ftp.uu.net:usenet/comp.sources.unix/volume10/cbw/ [FTPCP] soda.berkeley.edu:/pub/cypherpunks [FTPDF] ftp.funet.fi:pub/unix/security/destoo.tar.Z [FTPDQ] rsa.com:pub/faq/ [FTPEY] ftp.psy.uq.oz.au:pub/DES/ [FTPMD] rsa.com:? [FTPMR] ripem.msu.edu:pub/crypt/newdes.tar.Z [FTPNS] csrc.nist.gov:/bbs/nistpubs [FTPOB] ftp.3com.com:Orange-Book [FTPPF] prep.ai.mit.edu:pub/lpf/ [FTPPK] ucsd.edu:hamradio/packet/tcpip/crypto/des.tar.Z [FTPPX] ripem.msu.edu:pub/crypt/other/tran-and-prngxor.shar [FTPRF] nic.merit.edu:documents/rfc/ [FTPSF] beta.xerox.com:pub/hash/ [FTPSO] chalmers.se:pub/unix/des/des-2.2.tar.Z [FTPTR] ripem.msu.edu:pub/crypt/other/tran-and-prngxor.shar [FTPUF] ftp.uu.net:usenet/comp.sources.unix/volume28/ufc-crypt/ [FTPWP] garbo.uwasa.fi:pc/util/wppass2.zip World Wide Web pages: [WWWQC] http://www.quadralay.com/www/Crypt/Crypt.html Quadralay Cryptography archive [WWWVC] ftp://furmint.nectar.cs.cmu.edu/security/README.html Vince Cate's Cypherpunk Page 10.9. RFCs (available from [FTPRF]) [1424] B. Kaliski, Privacy Enhancement for Internet Electronic Mail: Part IV: Key Certification and Related Services. RFC 1424, February 1993. [1423] D. Balenson, Privacy Enhancement for Internet Electronic Mail: Part III: Algorithms, Modes, and Identifiers. RFC 1423, February 1993. [1422] S. Kent, Privacy Enhancement for Internet Electronic Mail: Part II: Certificate-Based Key Management. RFC 1422, February 1993. [1421] J. Linn, Privacy Enhancement for Internet Electronic Mail: Part I: Message Encryption and Authentication Procedures. RFC 1421, February 1993. 10.10. Related newsgroups There are other newsgroups which a sci.crypt reader might want also to read. Some have their own FAQs as well. alt.privacy.clipper Clipper, Capstone, Skipjack, Key Escrow alt.security general security discussions alt.security.index index to alt.security alt.security.pgp discussion of PGP alt.security.ripem discussion of RIPEM alt.society.civil-liberty general civil liberties, including privacy comp.compression discussion of compression algorithms and code comp.org.eff.news News reports from EFF comp.org.eff.talk discussion of EFF related issues comp.patents discussion of S/W patents, including RSA comp.risks some mention of crypto and wiretapping comp.society.privacy general privacy issues comp.security.announce announcements of security holes misc.legal.computing software patents, copyrights, computer laws sci.math general math discussion talk.politics.crypto politics of cryptography