Cryptography

Cryptography (or cryptology; from the greek words kryptos, "hidden, secret"; and gráphō, "I write", or -logia, respectively)Liddell and Scott's Greek-English Lexicon. Oxford University Press. (1984) is the practice and study of hiding information. Modern cryptography intersects the disciplines of mathematics, computer science, and engineering. Applications of cryptography include ATM cards, computer passwords, and electronic commerce.
==Terminology==
Until modern times cryptography referred almost exclusively to encryption, which is the process of converting ordinary information (plaintext) into unintelligible gibberish (i.e., ciphertext). Decryption is the reverse, in other words, moving from the unintelligible ciphertext back to plaintext. A cipher (or cypher) is a pair of algorithms which create the encryption and the reversing decryption. The detailed operation of a cipher is controlled both by the algorithm and in each instance by a key. This is a secret parameter (ideally known only to the communicants) for a specific message exchange context. Keys are important, as ciphers without variable keys can be trivially broken with only the knowledge of the cipher used and are therefore less than useful for most purposes. Historically, ciphers were often used directly for encryption or decryption without additional procedures such as authentication or integrity checks.
In colloquial use, the term "code" is often used to mean any method of encryption or concealment of meaning. However, in cryptography, code has a more specific meaning. It means the replacement of a unit of plaintext (i.e., a meaningful word or phrase) with a code word (for example, apple pie replaces attack at dawn). Codes are no longer used in serious cryptography—except incidentally for such things as unit designations (e.g., Bronco Flight or Operation Overlord) —- since properly chosen ciphers are both more practical and more secure than even the best codes and also are better adapted to computers.
Some use the terms cryptography and cryptology interchangeably in English, while others (including US military practice generally) use cryptography to refer specifically to the use and practice of cryptographic techniques and cryptology to refer to the combined study of cryptography and cryptanalysis.Oded Goldreich, Foundations of Cryptography, Volume 1: Basic Tools, Cambridge University Press, 2001, ISBN 0-521-79172-3 English is more flexible than several other languages in which cryptology (done by cryptologists) is always used in the second sense above. In the English Wikipedia the general term used for the entire field is cryptography (done by cryptographers). 
The study of characteristics of languages which have some application in cryptography (or cryptology), i.e. frequency data, letter combinations, universal patterns, etc. is called cryptolinguistics.
==History of cryptography and cryptanalysis==
Before the modern era, cryptography was concerned solely with message confidentiality (i.e., encryption) — conversion of messages from a comprehensible form into an incomprehensible one and back again at the other end, rendering it unreadable by interceptors or eavesdroppers without secret knowledge (namely the key needed for decryption of that message). Encryption was used to (attempt to) ensure secrecy in communications, such as those of spies, military leaders, and diplomats. In recent decades, the field has expanded beyond confidentiality concerns to include techniques for message integrity checking, sender/receiver identity authentication, digital signatures, interactive proofs and secure computation, among others.
===Classical cryptography===
The earliest forms of secret writing required little more than local pen and paper analogs, as most people could not read. More literacy, or literate opponents, required actual cryptography. The main classical cipher types are transposition ciphers, which rearrange the order of letters in a message (e.g., 'hello world' becomes 'ehlol owrdl' in a trivially simple rearrangement scheme), and substitution ciphers, which systematically replace letters or groups of letters with other letters or groups of letters (e.g., 'fly at once' becomes 'gmz bu podf' by replacing each letter with the one following it in the Latin alphabet). Simple versions of either offered little confidentiality from enterprising opponents, and still do. An early substitution cipher was the Caesar cipher, in which each letter in the plaintext was replaced by a letter some fixed number of positions further down the alphabet. It was named after Julius Caesar who is reported to have used it, with a shift of 3, to communicate with his generals during his military campaigns, just like EXCESS-3 code in boolean algebra. There is record of several early Hebrew ciphers as well. The earliest known use of cryptography is some carved ciphertext on stone in Egypt (ca 1900 BC), but this may have been done for the amusement of literate observers. The next oldest is bakery recipes from Mesopotamia. 
Cryptography is recommended in the Kama Sutra as a way for lovers to communicate without inconvenient discovery.Kama Sutra, Sir Richard F. Burton, translator, Part I, Chapter III, 44th and 45th arts. Steganography (i.e., hiding even the existence of a message so as to keep it confidential) was also first developed in ancient times. An early example, from Herodotus, concealed a message - a tattoo on a slave's shaved head - under the regrown hair.David Kahn, The Codebreakers, 1967, ISBN 0-684-83130-9. More modern examples of steganography include the use of invisible ink, microdots, and digital watermarks to conceal information. 
Ciphertexts produced by classical ciphers (and some modern ones) always reveal statistical information about the plaintext, which can often be used to break them. After the discovery of frequency analysis perhaps by the Arab mathematician and polymath, Al-Kindi (also known as Alkindus), in the 9th century, nearly all such ciphers became more or less readily breakable by any informed attacker. Such classical ciphers still enjoy popularity today, though mostly as puzzles (see cryptogram). Essentially all ciphers remained vulnerable to cryptanalysis using this technique until the development of the polyalphabetic cipher, most clearly by Leon Battista Alberti around the year 1467, though there is some indication that it was known to Al-Kindi.Ibrahim A. Al-Kadi (April 1992), "The origins of cryptology: The Arab contributions”, Cryptologia 16 (2): 97–126 Alberti's innovation was to use different ciphers (i.e., substitution alphabets) for various parts of a message (perhaps for each successive plaintext letter at the limit). He also invented what was probably the first automatic cipher device, a wheel which implemented a partial realization of his invention. In the polyalphabetic Vigenère cipher, encryption uses a key word, which controls letter substitution depending on which letter of the key word is used. In the mid 1800s Babbage showed that polyalphabetic ciphers of this type remained partially vulnerable to extended frequency analysis techniques.
Although frequency analysis is a powerful and general technique against many ciphers, encryption has still been often effective in practice; many a would-be cryptanalyst was unaware of the technique. Breaking a message without using frequency analysis essentially required knowledge of the cipher used and perhaps of the key involved, thus making espionage, bribery, burglary, defection, etc. more attractive approaches to the cryptanalyticly uninformed. It was finally explicitly recognized in the 19th century that secrecy of a cipher's algorithm is not a sensible nor practical safeguard of message security; in fact, it was further realized that any adequate cryptographic scheme (including ciphers) should remain secure even if the adversary fully understands the cipher algorithm itself. Security of the key used should alone be sufficient for a good cipher to maintain confidentiality under an attack. This fundamental principle was first explicitly stated in 1883 by Auguste Kerckhoffs and is generally called Kerckhoffs' principle; alternatively and more bluntly, it was restated by Claude Shannon, the inventor of information theory and the fundamentals of theoretical cryptography, as Shannon's Maxim — 'the enemy knows the system'.
Various physical devices and aids have been used to assist with ciphers. One of the earliest may have been the scytale of ancient Greece, a rod supposedly used by the Spartans as an aid for a transposition cipher (see image above). In medieval times, other aids were invented such as the cipher grille, which was also used for a kind of steganography. With the invention of polyalphabetic ciphers came more sophisticated aids such as Alberti's own cipher disk, Johannes Trithemius' tabula recta scheme, and Thomas Jefferson's multi-cylinder (not publicly known, and reinvented independently by Bazeries around 1900). Many mechanical encryption/decryption devices were invented early in the 20th century, and several patented, among them rotor machines — famously including the Enigma machine used by the German government and military from the late 20s and during World War II. The ciphers implemented by better quality examples of these machine designs brought about a substantial increase in cryptanalytic difficulty after WWI.James Gannon, Stealing Secrets, Telling Lies: How Spies and Codebreakers Helped Shape the Twentieth Century, Washington, D.C., Brassey's, 2001, ISBN 1-57488-367-4.
===The computer era===
The development of digital computers and electronics after WWII made possible much more complex ciphers. Furthermore, computers allowed for the encryption of any kind of data representable in any binary format, unlike classical ciphers which only encrypted written language texts; this was new and significant. Computer use has thus supplanted linguistic cryptography, both for cipher design and cryptanalysis. Many computer ciphers can be characterized by their operation on binary bit sequences (sometimes in groups or blocks), unlike classical and mechanical schemes, which generally manipulate traditional characters (i.e., letters and digits) directly. However, computers have also assisted cryptanalysis, which has compensated to some extent for increased cipher complexity. Nonetheless, good modern ciphers have stayed ahead of cryptanalysis; it is typically the case that use of a quality cipher is very efficient (i.e., fast and requiring few resources (ie, memory or CPU capability)), while breaking it requires an effort many orders of magnitude larger, and vastly larger than that required for any classical cipher, making cryptanalysis so inefficient and impractical as to be effectively impossible. Alternate methods of attack (bribery, burglary, threat, torture, ...) have become more attractive in consequence.
Extensive open academic research into cryptography is relatively recent; it began only in the mid-1970s. Medieval work was both less systematic, less comprehensive, and more likely to attract attention from the Church or others as Satanically inspired or dangerous to the state or those in power; at least two of Johannes Trithemius' books were added to the Index of banned books by the Roman Catholic Church. In recent times, IBM personnel designed the algorithm that became the Federal (ie, US) Data Encryption Standard; Whitfield Diffie and Martin Hellman published their key agreement algorithm,Whitfield Diffie and Martin Hellman, "New Directions in Cryptography", IEEE Transactions on Information Theory, vol. IT-22, Nov. 1976, pp: 644–654. (pdf); and the RSA algorithm was published in Martin Gardner's Scientific American column. Since then, cryptography has become a widely used tool in communications, computer networks, and computer security generally. Some modern cryptographic techniques can only keep their keys secret if certain mathematical problems are intractable, such as the integer factorisation or the discrete logarithm problems, so there are deep connections with abstract mathematics. There are no absolute proofs that a cryptographic technique is secure (but see one-time pad); at best, there are proofs that some techniques are secure if some computational problem is difficult to solve, or this or that assumption about implementation or practical use is met.
As well as being aware of cryptographic history, cryptographic algorithm and system designers must also sensibly consider probable future developments while working on their designs. For instance, continuous improvements in computer processing power have increased the scope of brute-force attacks, thus when specifying key lengths, the required key lengths are similarly advancing. The potential effects of quantum computing are already being considered by some cryptographic system designers; the announced imminence of small implementations of these machines may be making the need for this preemptive caution rather more than merely speculative.AJ Menezes, PC van Oorschot, and SA Vanstone, Handbook of Applied Cryptography ISBN 0-8493-8523-7.
Essentially, prior to the early 20th century, cryptography was chiefly concerned with linguistic and lexicographic patterns. Since then the emphasis has shifted, and cryptography now makes extensive use of mathematics, including aspects of information theory, computational complexity, statistics, combinatorics, abstract algebra, number theory, and finite mathematics generally. Cryptography is, also, a branch of engineering, but an unusual one as it deals with active, intelligent, and malevolent opposition (see cryptographic engineering and security engineering); other kinds of engineering (eg, civil or chemical engineering) need deal only with neutral natural forces. There is also active research examining the relationship between cryptographic problems and quantum physics (see quantum cryptography and quantum computing).
==Modern cryptography==
The modern field of cryptography can be divided into several areas of study. The chief ones are discussed here; see Topics in Cryptography for more.
===Symmetric-key cryptography===
Symmetric-key cryptography refers to encryption methods in which both the sender and receiver share the same key (or, less commonly, in which their keys are different, but related in an easily computable way). This was the only kind of encryption publicly known until June 1976.
The modern study of symmetric-key ciphers relates mainly to the study of block ciphers and stream ciphers and to their applications. A block cipher is, in a sense, a modern embodiment of Alberti's polyalphabetic cipher: block ciphers take as input a block of plaintext and a key, and output a block of ciphertext of the same size. Since messages are almost always longer than a single block, some method of knitting together successive blocks is required. Several have been developed, some with better security in one aspect or another than others. They are the modes of operation and must be carefully considered when using a block cipher in a cryptosystem.
The Data Encryption Standard (DES) and the Advanced Encryption Standard (AES) are block cipher designs which have been designated cryptography standards by the US government (though DES's designation was finally withdrawn after the AES was adopted).FIPS PUB 197: The official Advanced Encryption Standard. Despite its deprecation as an official standard, DES (especially its still-approved and much more secure triple-DES variant) remains quite popular; it is used across a wide range of applications, from ATM encryptionNCUA letter to credit unions, July 2004 to e-mail privacyRFC 2440 - Open PGP Message Format and secure remote access.SSH at windowsecurity.com by Pawel Golen, July 2004 Many other block ciphers have been designed and released, with considerable variation in quality. Many have been thoroughly broken. See Category:Block ciphers.Bruce Schneier, Applied Cryptography, 2nd edition, Wiley, 1996, ISBN 0-471-11709-9.
Stream ciphers, in contrast to the 'block' type, create an arbitrarily long stream of key material, which is combined with the plaintext bit-by-bit or character-by-character, somewhat like the one-time pad. In a stream cipher, the output stream is created based on a hidden internal state which changes as the cipher operates. That internal state is initially set up using the secret key material. RC4 is a widely used stream cipher; see Category:Stream ciphers. Block ciphers can be used as stream ciphers; see Block cipher modes of operation.
Cryptographic hash functions are a third type of cryptographic algorithm. They take a message of any length as input, and output a short, fixed length hash which can be used in (for example) a digital signature. For good hash functions, an attacker cannot find two messages that produce the same hash. MD4 is a long-used hash function which is now broken; MD5, a strengthened variant of MD4, is also widely used but broken in practice. The U.S. National Security Agency developed the Secure Hash Algorithm series of MD5-like hash functions: SHA-0 was a flawed algorithm that the agency withdrew; SHA-1 is widely deployed and more secure than MD5, but cryptanalysts have identified attacks against it; the SHA-2 family improves on SHA-1, but it isn't yet widely deployed, and the U.S. standards authority thought it "prudent" from a security perspective to develop a new standard to "significantly improve the robustness of NIST's overall hash algorithm toolkit."National Institute of Standards and Technology Thus, a hash function design competition is underway and meant to select a new U.S. national standard, to be called SHA-3, by 2012.
Message authentication codes (MACs) are much like cryptographic hash functions, except that a secret key is used to authenticate the hash value on receipt.
===Public-key cryptography===
Symmetric-key cryptosystems use the same key for encryption and decryption of a message, though a message or group of messages may have a different key than others. A significant disadvantage of symmetric ciphers is the key management necessary to use them securely. Each distinct pair of communicating parties must, ideally, share a different key, and perhaps each ciphertext exchanged as well. The number of keys required increases as the square of the number of network members, which very quickly requires complex key management schemes to keep them all straight and secret. The difficulty of securely establishing a secret key between two communicating parties, when a secure channel doesn't already exist between them, also presents a chicken-and-egg problem which is a considerable practical obstacle for cryptography users in the real world.
In a groundbreaking 1976 paper, Whitfield Diffie and Martin Hellman proposed the notion of public-key (also, more generally, called asymmetric key) cryptography in which two different but mathematically related keys are used — a public key and a private key.Whitfield Diffie and Martin Hellman, "Multi-user cryptographic techniques" [Diffie and Hellman, AFIPS Proceedings 45, pp109–112, June 8, 1976]. A public key system is so constructed that calculation of one key (the 'private key') is computationally infeasible from the other (the 'public key'), even though they are necessarily related. Instead, both keys are generated secretly, as an interrelated pair.Ralph Merkle was working on similar ideas at the time and encountered publication delays, and Hellman has suggested that the term used should be Diffie-Hellman-Merkle aysmmetric key cryptography. The historian David Kahn described public-key cryptography as "the most revolutionary new concept in the field since polyalphabetic substitution emerged in the Renaissance".David Kahn, "Cryptology Goes Public", 58 Foreign Affairs 141, 151 (fall 1979), p. 153.
In public-key cryptosystems, the public key may be freely distributed, while its paired private key must remain secret. The public key is typically used for encryption, while the private or secret key is used for decryption. Diffie and Hellman showed that public-key cryptography was possible by presenting the Diffie-Hellman key exchange protocol. 
In 1978, Ronald Rivest, Adi Shamir, and Len Adleman invented RSA, another public-key system.R. Rivest, A. Shamir, L. Adleman. A Method for Obtaining Digital Signatures and Public-Key Cryptosystems. Communications of the ACM, Vol. 21 (2), pp.120–126. 1978. Previously released as an MIT "Technical Memo" in April 1977, and published in Martin Gardner's Scientific American Mathematical recreations column 
In 1997, it finally became publicly known that asymmetric key cryptography had been invented by James H. Ellis at GCHQ, a British intelligence organization, and that, in the early 1970s, both the Diffie-Hellman and RSA algorithms had been previously developed (by Malcolm J. Williamson and Clifford Cocks, respectively).Clifford Cocks. A Note on 'Non-Secret Encryption', CESG Research Report, 20 November 1973.
The Diffie-Hellman and RSA algorithms, in addition to being the first publicly known examples of high quality public-key algorithms, have been among the most widely used. Others include the Cramer-Shoup cryptosystem, ElGamal encryption, and various elliptic curve techniques. See Category:Asymmetric-key cryptosystems.
 
In addition to encryption, public-key cryptography can be used to implement digital signature schemes. A digital signature is reminiscent of an ordinary signature; they both have the characteristic that they are easy for a user to produce, but difficult for anyone else to forge. Digital signatures can also be permanently tied to the content of the message being signed; they cannot then be 'moved' from one document to another, for any attempt will be detectable. In digital signature schemes, there are two algorithms: one for signing, in which a secret key is used to process the message (or a hash of the message, or both), and one for verification, in which the matching public key is used with the message to check the validity of the signature. RSA and DSA are two of the most popular digital signature schemes. Digital signatures are central to the operation of public key infrastructures and many network security schemes (eg, SSL/TLS, many VPNs, etc).
Public-key algorithms are most often based on the computational complexity of "hard" problems, often from number theory. For example, the hardness of RSA is related to the integer factorization problem, while Diffie-Hellman and DSA are related to the discrete logarithm problem. More recently, elliptic curve cryptography has developed in which security is based on number theoretic problems involving elliptic curves. Because of the difficulty of the underlying problems, most public-key algorithms involve operations such as modular multiplication and exponentiation, which are much more computationally expensive than the techniques used in most block ciphers, especially with typical key sizes. As a result, public-key cryptosystems are commonly hybrid cryptosystems, in which a fast high-quality symmetric-key encryption algorithm is used for the message itself, while the relevant symmetric key is sent with the message, but encrypted using a public-key algorithm. Similarly, hybrid signature schemes are often used, in which a cryptographic hash function is computed, and only the resulting hash is digitally signed.
===Cryptanalysis===
thumb|250px|Poznań monument (center) to Polish cryptologists whose breaking of Germany's Enigma machine ciphers, beginning in 1932, altered the course of World War II
The goal of cryptanalysis is to find some weakness or insecurity in a cryptographic scheme, thus permitting its subversion or evasion. 
It is a commonly held misconception that every encryption method can be broken. In connection with his WWII work at Bell Labs, Claude Shannon proved that the one-time pad cipher is unbreakable, provided the key material is truly random, never reused, kept secret from all possible attackers, and of equal or greater length than the message."Shannon": Claude Shannon and Warren Weaver, "The Mathematical Theory of Communication", University of Illinois Press, 1963, ISBN 0-252-72548-4 Most ciphers, apart from the one-time pad, can be broken with enough computational effort by brute force attack, but the amount of effort needed may be exponentially dependent on the key size, as compared to the effort needed to use the cipher. In such cases, effective security could be achieved if it is proven that the effort required (i.e., "work factor", in Shannon's terms) is beyond the ability of any adversary. This means it must be shown that no efficient method (as opposed to the time-consuming brute force method) can be found to break the cipher. Since no such showing can be made currently, as of today, the one-time-pad remains the only theoretically unbreakable cipher.
There are a wide variety of cryptanalytic attacks, and they can be classified in any of several ways. A common distinction turns on what an attacker knows and what capabilities are available. In a ciphertext-only attack, the cryptanalyst has access only to the ciphertext (good modern cryptosystems are usually effectively immune to ciphertext-only attacks). In a known-plaintext attack, the cryptanalyst has access to a ciphertext and its corresponding plaintext (or to many such pairs). In a chosen-plaintext attack, the cryptanalyst may choose a plaintext and learn its corresponding ciphertext (perhaps many times); an example is gardening, used by the British during WWII. Finally, in a chosen-ciphertext attack, the cryptanalyst may be able to choose ciphertexts and learn their corresponding plaintexts. Also important, often overwhelmingly so, are mistakes (generally in the design or use of one of the protocols involved; see Cryptanalysis of the Enigma for some historical examples of this).
Cryptanalysis of symmetric-key ciphers typically involves looking for attacks against the block ciphers or stream ciphers that are more efficient than any attack that could be against a perfect cipher. For example, a simple brute force attack against DES requires one known plaintext and 255 decryptions, trying approximately half of the possible keys, to reach a point at which chances are better than even the key sought will have been found. But this may not be enough assurance; a linear cryptanalysis attack against DES requires 243 known plaintexts and approximately 243 DES operations.Pascal Junod, "On the Complexity of Matsui's Attack", SAC 2001. This is a considerable improvement on brute force attacks.
Public-key algorithms are based on the computational difficulty of various problems. The most famous of these is integer factorization (e.g., the RSA algorithm is based on a problem related to integer factoring), but the discrete logarithm problem is also important. Much public-key cryptanalysis concerns numerical algorithms for solving these computational problems, or some of them, efficiently (ie, in a practical time). For instance, the best known algorithms for solving the elliptic curve-based version of discrete logarithm are much more time-consuming than the best known algorithms for factoring, at least for problems of more or less equivalent size. Thus, other things being equal, to achieve an equivalent strength of attack resistance, factoring-based encryption techniques must use larger keys than elliptic curve techniques. For this reason, public-key cryptosystems based on elliptic curves have become popular since their invention in the mid-1990s.
While pure cryptanalysis uses weaknesses in the algorithms themselves, other attacks on cryptosystems are based on actual use of the algorithms in real devices, and are called side-channel attacks. If a cryptanalyst has access to, say, the amount of time the device took to encrypt a number of plaintexts or report an error in a password or PIN character, he may be able to use a timing attack to break a cipher that is otherwise resistant to analysis. An attacker might also study the pattern and length of messages to derive valuable information; this is known as traffic analysis,Dawn Song, David Wagner, and Xuqing Tian, "Timing Analysis of Keystrokes and Timing Attacks on SSH", In Tenth USENIX Security Symposium, 2001. and can be quite useful to an alert adversary. Poor administration of a cryptosystem, such as permitting too short keys, will make any system vulnerable, regardless of other virtues. And, of course, social engineering, and other attacks against the personnel who work with cryptosystems or the messages they handle (e.g., bribery, extortion, blackmail, espionage, torture, ...) may be the most productive attacks of all.
===Cryptographic primitives===
Much of the theoretical work in cryptography concerns cryptographic primitives — algorithms with basic cryptographic properties — and their relationship to other cryptographic problems. More complicated cryptographic tools are then built from these basic primitives. These primitives provide fundamental properties, which are used to develop more complex tools called cryptosystems or cryptographic protocols, which guarantee one or more high-level security properties. Note however, that the distinction between cryptographic primitives and cryptosystems, is quite arbitrary; for example, the RSA algorithm is sometimes considered a cryptosystem, and sometimes a primitive. Typical examples of cryptographic primitives include pseudorandom functions, one-way functions, etc.
===Cryptosystems===
One or more cryptographic primitives are often used to develop a more complex algorithm, called a cryptographic system, or cryptosystem. Cryptosystems (e.g. El-Gamal encryption) are designed to provide particular functionality (e.g. public key encryption) while guaranteeing certain security properties (e.g. CPA security in the random oracle model). Cryptosystems use the properties of the underlying cryptographic primitives to support the system's security properties. Of course, as the distinction between primitives and cryptosystems is somewhat arbitrary, a sophisticated cryptosystem can be derived from a combination of several more primitive cryptosystems. In many cases, the cryptosystem's structure involves back and forth communication among two or more parties in space (e.g., between the sender of a secure message and its receiver) or across time (e.g., cryptographically protected backup data). Such cryptosystems are sometimes called cryptographic protocols.
Some widely known cryptosystems include RSA encryption, Schnorr signature, El-Gamal encryption, PGP, etc. More complex cryptosystems include electronic cashS. Brands, "Untraceable Off-line Cash in Wallets with Observers", In Advances in Cryptology — Proceedings of CRYPTO, Springer-Verlag, 1994. systems, signcryption systems, etc. Some more 'theoretical' cryptosystems include interactive proof systems,László Babai. "Trading group theory for randomness". Proceedings of the Seventeenth Annual Symposium on the Theory of Computing, ACM, 1985. (like zero-knowledge proofs,S. Goldwasser, S. Micali, and C. Rackoff, "The Knowledge Complexity of Interactive Proof Systems", SIAM J. Computing, vol. 18, num. 1, pp. 186–208, 1989.), systems for secret sharingG. Blakley. "Safeguarding cryptographic keys." In Proceedings of AFIPS 1979, volume 48, pp. 313–317, June 1979.A. Shamir. "How to share a secret." In Communications of the ACM, volume 22, pp. 612–613, ACM, 1979., etc.
Until recently, most security properties of most cryptosystems were demonstrated using empirical techniques, or using ad hoc reasoning. Recently, there has been considerable effort to develop formal techniques for establishing the security of cryptosystems; this has been generally called provable security. The general idea of provable security is to give arguments about the computational difficulty needed to compromise some security aspect of the cryptosystem (ie, to any adversary).
The study of how best to implement and integrate cryptography in software applications is itself a distinct field, see: cryptographic engineering and security engineering.
==Legal issues==
===Prohibitions===
Cryptography has long been of interest to intelligence gathering and law enforcement agencies. Actually secret communications may be criminal or even treasonous; those whose communications are open to inspection may be less likely to be either. Because of its facilitation of privacy, and the diminution of privacy attendant on its prohibition, cryptography is also of considerable interest to civil rights supporters. Accordingly, there has been a history of controversial legal issues surrounding cryptography, especially since the advent of inexpensive computers has made widespread access to high quality cryptography possible. 
In some countries, even the domestic use of cryptography is, or has been, restricted. Until 1999, France significantly restricted the use of cryptography domestically, though it has relaxed many of these. In China, a license is still required to use cryptography. Many countries have tight restrictions on the use of cryptography. Among the more restrictive are laws in Belarus, Kazakhstan, Mongolia, Pakistan, Russia, Singapore, Tunisia, and Vietnam.RSA Laboratories' Frequently Asked Questions About Today's Cryptography 
In the United States, cryptography is legal for domestic use, but there has been much conflict over legal issues related to cryptography. One particularly important issue has been the export of cryptography and cryptographic software and hardware. Probably because of the importance of cryptanalysis in World War II and an expectation that cryptography would continue to be important for national security, many Western governments have, at some point, strictly regulated export of cryptography. After World War II, it was illegal in the US to sell or distribute encryption technology overseas; in fact, encryption was designated as auxiliary military equipment and put on the United States Munitions List.Cryptography & Speech from Cyberlaw Until the development of the personal computer, asymmetric key algorithms (ie, public key techniques), and the Internet, this was not especially problematic. However, as the Internet grew and computers became more widely available, high quality encryption techniques became well-known around the globe. As a result, export controls came to be seen to be an impediment to commerce and to research.
===Export controls===
In the 1990s, there were several challenges to US export regulations of cryptography. One involved Philip Zimmermann's Pretty Good Privacy (PGP) encryption program; it was released in the US, together with its source code, and found its way onto the Internet in June 1991. After a complaint by RSA Security (then called RSA Data Security, Inc., or RSADSI), Zimmermann was criminally investigated by the Customs Service and the FBI for several years. No charges were ever filed, however."Case Closed on Zimmermann PGP Investigation", press note from the IEEE. Also, Daniel Bernstein, then a graduate student at UC Berkeley, brought a lawsuit against the US government challenging some aspects of the restrictions based on free speech grounds. The 1995 case Bernstein v. United States ultimately resulted in a 1999 decision that printed source code for cryptographic algorithms and systems was protected as free speech by the United States Constitution.Bernstein v USDOJ, 9th Circuit court of appeals decision.
In 1996, thirty-nine countries signed the Wassenaar Arrangement, an arms control treaty that deals with the export of arms and "dual-use" technologies such as cryptography. The treaty stipulated that the use of cryptography with short key-lengths (56-bit for symmetric encryption, 512-bit for RSA) would no longer be export-controlled.The Wassenaar Arrangement on Export Controls for Conventional Arms and Dual-Use Goods and Technologies Cryptography exports from the US are now much less strictly regulated than in the past as a consequence of a major relaxation in 2000; there are no longer very many restrictions on key sizes in US-exported mass-market software. In practice today, since the relaxation in US export restrictions, and because almost every personal computer connected to the Internet, everywhere in the world, includes US-sourced web browsers such as Mozilla Firefox or Microsoft Internet Explorer, almost every Internet user worldwide has access to quality cryptography (i.e., when using sufficiently long keys with properly operating and unsubverted software, etc) in their browsers; examples are Transport Layer Security or SSL stack. The Mozilla Thunderbird and Microsoft Outlook E-mail client programs similarly can connect to IMAP or POP servers via TLS, and can send and receive email encrypted with S/MIME. Many Internet users don't realize that their basic application software contains such extensive cryptosystems. These browsers and email programs are so ubiquitous that even governments whose intent is to regulate civilian use of cryptography generally don't find it practical to do much to control distribution or use of cryptography of this quality, so even when such laws are in force, actual enforcement is often effectively impossible.
===NSA involvement===
Another contentious issue connected to cryptography in the United States is the influence of the National Security Agency on cipher development and policy. NSA was involved with the design of DES during its development at IBM and its consideration by the National Bureau of Standards as a possible Federal Standard for cryptography."The Data Encryption Standard (DES)" from Bruce Schneier's CryptoGram newsletter, June 15, 2000 DES was designed to be resistant to differential cryptanalysis,
 a powerful and general cryptanalytic technique known to NSA and IBM, that became publicly known only when it was rediscovered in the late 1980s.E. Biham and A. Shamir, "Differential cryptanalysis of DES-like cryptosystems", Journal of Cryptology, vol. 4 num. 1, pp. 3–72, Springer-Verlag, 1991. According to Steven Levy, IBM rediscovered differential cryptanalysis,Levy, pg. 56 but kept the technique secret at NSA's request. The technique became publicly known only when Biham and Shamir re-rediscovered and announced it some years later. The entire affair illustrates the difficulty of determining what resources and knowledge an attacker might actually have. 
Another instance of NSA's involvement was the 1993 Clipper chip affair, an encryption microchip intended to be part of the Capstone cryptography-control initiative. Clipper was widely criticized by cryptographers for two reasons. The cipher algorithm was then classified (the cipher, called Skipjack, though it was declassified in 1998 long after the Clipper initiative lapsed). The secret cipher caused concerns that NSA had deliberately made the cipher weak in order to assist its intelligence efforts. The whole initiative was also criticized based on its violation of Kerckhoffs' principle, as the scheme included a special escrow key held by the government for use by law enforcement, for example in wiretaps.
===Digital rights management===
Cryptography is central to digital rights management (DRM), a group of techniques for technologically controlling use of copyrighted material, being widely implemented and deployed at the behest of some copyright holders. In 1998, American President Bill Clinton signed the Digital Millennium Copyright Act (DMCA), which criminalized all production, dissemination, and use of certain cryptanalytic techniques and technology (now known or later discovered); specifically, those that could be used to circumvent DRM technological schemes.Digital Millennium Copyright Act This had a noticeable impact on the cryptography research community since an argument can be made that any cryptanalytic research violated, or might violate, the DMCA. Similar statutes have since been enacted in several countries and regions, including the implementation in the EU Copyright Directive. Similar restrictions are called for by treaties signed by World Intellectual Property Organization member-states.
The United States Department of Justice and FBI have not enforced the DMCA as rigorously as had been feared by some, but the law, nonetheless, remains a controversial one. One well-respected cryptography researcher, Niels Ferguson, has publicly statedhttp://www.macfergus.com/niels/dmca/cia.html that he will not release some of his research into an Intel security design for fear of prosecution under the DMCA, and both Alan Cox (longtime number 2 in Linux kernel development) and Professor Edward Felten (and some of his students at Princeton) have encountered problems related to the Act. Dmitry Sklyarov was arrested during a visit to the US from Russia, and jailed for some months for alleged violations of the DMCA which had occurred in Russia, where the work for which he was arrested and charged was then, and when he was arrested, legal. In 2007, the cryptographic keys responsible for Blu Ray and HD DVD content scrambling were discovered and released onto the internet. Both times, the MPAA sent out numerous DMCA takedown notices, and there was a massive internet backlash as a result of the implications of such notices on fair use and free speech both legally protected in the US and in some other jurisdictions.
==See also==
* Books on cryptography
* Watermarking
* Watermark detection
* :Category:Cryptographers
* Encyclopedia of Cryptography and Security
* List of cryptographers
* List of important publications in computer science#Cryptography
* Topics in cryptography
* Cipher System Identification
* Unsolved problems in computer science
* CrypTool Most widespread e-learning program about cryptography and cryptanalysis, open source
* List of multiple discoveries (see "RSA")
== Notes ==
== Further reading ==
* Excellent coverage of many classical ciphers and cryptography concepts and of the "modern" DES and RSA systems.
* Cryptography and Mathematics by Bernhard Esslinger, 200 pages, part of the free open-source package CrypTool, PDF download.
* In Code: A Mathematical Journey by Sarah Flannery (with David Flannery). Popular account of Sarah's award-winning project on public-key cryptography, co-written with her father.
* James Gannon, Stealing Secrets, Telling Lies: How Spies and Codebreakers Helped Shape the Twentieth Century, Washington, D.C., Brassey's, 2001, ISBN 1-57488-367-4.
* Oded Goldreich, Foundations of Cryptography, in two volumes, Cambridge University Press, 2001 and 2004.
* Introduction to Modern Cryptography by Jonathan Katz and Yehuda Lindell. .
* Alvin's Secret Code by Clifford B. Hicks (children's novel that introduces some basic cryptography and cryptanalysis).
* Ibrahim A. Al-Kadi, "The Origins of Cryptology: the Arab Contributions," Cryptologia, vol. 16, no. 2 (April 1992), pp. 97–126.
* Handbook of Applied Cryptography by A. J. Menezes, P. C. van Oorschot, and S. A. Vanstone CRC Press, (PDF download available), somewhat more mathematical than Schneier's Applied Cryptography.
* Andreas Pfitzmann: Security in IT Networks: Multilateral Security in Distributed and by Distributed Systems
* Introduction to Modern Cryptography by Phillip Rogaway and Mihir Bellare, a mathematical introduction to theoretical cryptography including reduction-based security proofs. PDF download.
* Cryptonomicon by Neal Stephenson (novel, WW2 Enigma cryptanalysis figures into the story, though not always realistically).
* Johann-Christoph Woltag, 'Coded Communications (Encryption)' in Rüdiger Wolfrum (ed) Max Planck Encyclopedia of Public International Law (Oxford University Press 2009). *, giving an overview of international law issues regarding cryptography.
== External links ==
* Crypto Glossary and Dictionary of Technical Cryptography
* Attack/Prevention Resource for Cryptography Whitepapers, Tools, Videos, and Podcasts.
* Cryptography: The Ancient Art of Secret Messages by Monica Pawlan - February 1998
* Handbook of Applied Cryptography by A. J. Menezes, P. C. van Oorschot, and S. A. Vanstone (PDF download available), somewhat more mathematical than Schneier's book.
* NSA's CryptoKids.
* Overview and Applications of Cryptology by the CrypTool Team; PDF; 3.8 MB—July 2008
* RSA Laboratories' frequently asked questions about today's cryptography
* sci.crypt mini-FAQ
* 
 
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