# Cryptography

### From Wikipedia, the free encyclopedia

**Cryptography**(or cryptology; derived from Greek κρυπτός

*kryptós*"hidden," and the verb γράφω

*gráfo*"write" or λεγειν

*legein*"to speak") is the practice and study of hiding information. In modern times, cryptography is considered to be a branch of both mathematics and computer science, and is affiliated closely with information theory, computer security, and engineering

^{[citation needed]}. Cryptography is used in applications present in technologically advanced societies; examples include the security of ATM cards, computer passwords, and electronic commerce, which all depend on cryptography

^{[citation needed]}.

## Contents[hide] |

## [edit] Terminology

Until modern times, cryptography referred almost exclusively to

*encryption*, the process of converting ordinary information (plaintext) into unintelligible gibberish (ie,*ciphertext*).^{[1]}Decryption is the reverse, moving from unintelligible ciphertext to plaintext. A*cipher*(or*cypher*) is a pair of algorithms which perform this 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 are trivially breakable and 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 (eg, 'Bronco Flight' or Operation Overlord) —- since properly chosen ciphers are both more practical and more secure than even the best codes, and better adapted to computers as well.Some use the terms

*cryptography*and*cryptology*interchangeably in English, while others use*cryptography*to refer to the use and practice of cryptographic techniques, and*cryptology*to refer to the subject as a field of study.^{[2]}## [edit] History of cryptography and cryptanalysis

sender/receiver identity authentication, digital signatures, interactive proofs, and secure computation, amongst others.

The earliest forms of secret writing required little more than local pen and paper analogs, as most people could not read. More literacy, or opponent literacy, required actual cryptography. The main classical cipher types are transposition ciphers, which rearrange the order of letters in a message (e.g. 'help me' becomes 'ehpl em' 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 alphabet). Simple versions of either offered little confidentiality from enterprising opponents, and still don't. 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.

Encryption attempts to ensure secrecy in communications, such as those of spies, military leaders, and diplomats, but it has also had religious applications. For instance, early Christians used cryptography to obfuscate some aspects of their religious writings to avoid the near certain persecution they would have faced had they been less cautious; famously, 666 or in some early manuscripts, 616, the Number of the Beast from the Christian New Testament Book of Revelation, is sometimes thought to be a ciphertext referring to the Roman Emperor Nero, one of whose policies was persecution of Christians.

^{[3]}There is record of several, even earlier, Hebrew ciphers as well. Cryptography is recommended in the Kama Sutra as a way for lovers to communicate without inconvenient discovery.^{[4]}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.^{[1]}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 polymath al-Kindi) about the 9th century, nearly all such ciphers became more or less readily breakable by an 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 invention of the polyalphabetic cipher, most clearly by Leon Battista Alberti around the year 1467 (though there is some indication of earlier Arab knowledge of them). Alberti's innovation was to use different ciphers (i.e., substitution alphabets) for various parts of a message (perhaps for each successive plaintext letter in 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 frequency analysis techniques.^{[1]}Although frequency analysis is a powerful and general technique, encryption was still often effective in practice; many a would-be cryptanalyst was unaware of the technique. Breaking a message without frequency analysis essentially required knowledge of the cipher used, thus encouraging espionage, bribery, burglary, defection, etc. to discover it. It was finally explicitly recognized in the 19th century that secrecy of a cipher's algorithm is not a sensible or practical safeguard; in fact, it was further realized any adequate cryptographic scheme (including ciphers) should remain secure even if the adversary fully understands the cipher algorithm itself. Secrecy of the key should alone be sufficient for a good ciphers to maintain confidentiality under 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 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. In medieval times, other aids were invented such as the cipher grille, 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 (reinvented independently by Bazeries around 1900). Several mechanical encryption/decryption devices were invented early in the 20th century, and many patented, including rotor machines — most famously the Enigma machine used by Germany in World War II. The ciphers implemented by better quality examples of these designs brought about a substantial increase in cryptanalytic difficulty after WWI.

^{[5]}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 that is represented by computers in any binary format, unlike classical ciphers which only encrypted written language texts, dissolving the utility of a linguistic approach to cryptanalysis in many cases. 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 usually the case that use of a quality cipher is very efficient (i.e., fast and requiring few resources), while breaking it requires an effort many orders of magnitude larger, making cryptanalysis so inefficient and impractical as to be effectively impossible.
Extensive open academic research into cryptography is relatively recent — it began only in the mid-1970s with the public specification of DES (the Data Encryption Standard) by the NBS, the Diffie-Hellman paper,

^{[6]}and the public release of the RSA algorithm. Since then, cryptography has become a widely used tool in communications, computer networks, and computer security generally. The present security level of many modern cryptographic techniques is based on the difficulty of certain computational problems, such as the integer factorisation problem or the discrete logarithm problem. In many cases, there are proofs that cryptographic techniques are secure*if*a certain computational problem cannot be solved efficiently.^{[2]}With one notable exception—the one-time pad—these proofs are contingent, and thus not definitive, but are currently the best available for cryptographic algorithms and protocols.As well as being aware of cryptographic history, cryptographic algorithm and system designers must also sensibly consider probable future developments in their designs. For instance, the continued improvements in computer processing power have increased the scope of brute-force attacks when specifying key lengths. The potential effects of quantum computing are already being considered by some cryptographic system designers; the announced imminence of small implementations of these machines is making the need for this preemptive caution fully explicit.

^{[7]}Essentially, prior to the early 20th century, cryptography was chiefly concerned with linguistic 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, and number theory. 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); most other kinds of 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).

## [edit] 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.

### [edit] Symmetric-key cryptography

^{[6]}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 mode of operations 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).

^{[8]}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 encryption^{[9]}to e-mail privacy^{[10]}and secure remote access.^{[11]}Many other block ciphers have been designed and released, with considerable variation in quality. Many have been thoroughly broken. See Category:Block ciphers.^{[7]}^{[12]}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 an internal state which changes as the cipher operates. That state's change is controlled by the key, and, in some stream ciphers, by the plaintext stream as well. RC4 is an example of a well-known stream cipher; see Category:Stream ciphers.

^{[7]}Cryptographic hash functions (often called

*message digest functions*) do not necessarily use keys, but are a related and important class of cryptographic algorithms. They take input data (often an entire message), and output a short, fixed length hash, and do so as a one-way function. For good ones, collisions (two plaintexts which produce the same hash) are extremely difficult to find.Message authentication codes (MACs) are much like cryptographic hash functions, except that a secret key is used to authenticate the hash value

^{[7]}on receipt.### [edit] Public-key cryptography

*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.

^{[13]}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.

^{[14]}The historian David Kahn described public-key cryptography as "the most revolutionary new concept in the field since polyalphabetic substitution emerged in the Renaissance".

^{[15]}

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.^{[6]}In 1997, it finally became publicly known that asymmetric key cryptography had been invented by James H. Ellis at GCHQ, a British intelligence organization, in the early 1970s, and that both the Diffie-Hellman and RSA algorithms had been previously developed (by Malcolm J. Williamson and Clifford Cocks, respectively).

^{[17]}The Diffie-Hellman and RSA algorithms, in addition to being the first publicly known examples of high quality public-key ciphers, 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 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 (SSL/TLS, many VPNs, etc).^{[12]}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.^{[7]}### [edit] Cryptanalysis

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.

^{[18]}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 (ie, '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

*choose*ciphertexts and learn their corresponding plaintexts.^{[7]}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 2

^{55}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 2^{43}known plaintexts and approximately 2^{43}DES operations.^{[19]}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 (eg, the RSA algorithm is based on a problem related to 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. 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,^{[20]}and can be quite useful to an alert adversary. 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, ...) may be the most productive attacks of all.### [edit] Cryptographic primitives

Much of the theoretical work in cryptography concerns cryptographic

*primitives*— algorithms with basic cryptographic properties — and their relationship to other cryptographic problems. For example, a one-way function is a function intended to be easy to compute but hard to invert. In a very general sense, for any cryptographic application to be secure (if based on such computational feasibility assumptions), one-way functions must exist. However, if one-way functions exist, this implies that P ≠ NP.^{[2]}Since the P versus NP problem is currently unsolved, it is not known if one-way functions really do exist. More complicated cryptographic tools are then built from these basic primitives. For instance, if one-way functions exist, then secure pseudorandom generators and secure pseudorandom functions exist.^{[21]}Complex functionality in an application must be built in using combinations of these algorithms and assorted protocols. Such combinations are called cryptosystems and it is they which users will encounter. Examples include PGP and its variants, ssh, SSL/TLS, all PKIs, digital signatures, etc

Other cryptographic primitives include the encryption algorithms themselves, one-way permutations, trapdoor permutations, etc.

### [edit] Cryptographic protocols

In many cases, cryptographic techniques involve back and forth communication among two or more parties in space (eg, between the home office and a branch office) or across time (e.g., cryptographically protected backup data). The term

*cryptographic protocol*captures this general idea.Cryptographic protocols have been developed for a wide range of problems, including relatively simple ones like interactive proof systems,

^{[22]}secret sharing,^{[23]}^{[24]}and zero-knowledge proofs,^{[25]}and much more complex ones like electronic cash^{[26]}and secure multiparty computation.^{[27]}When the security of a good cryptographic system fails, it is rare that the vulnerability leading to the breach will have been in a quality cryptographic primitive. Instead, weaknesses are often mistakes in the protocol design (often due to inadequate design procedures, or less than thoroughly informed designers), in the implementation (e.g., a software bug), in a failure of the assumptions on which the design was based (e.g., proper training of those who will be using the system), or some other human error. Many cryptographic protocols have been designed and analyzed using

*ad hoc*methods, but they rarely have any proof of security. Methods for formally analyzing the security of protocols, based on techniques from mathematical logic (see for example BAN logic), and more recently from concrete security principles, have been the subject of research for the past few decades.^{[28]}^{[29]}^{[30]}Unfortunately, to date these tools have been cumbersome and are not widely used for complex designs.The study of how best to implement and integrate cryptography in applications is itself a distinct field, see: cryptographic engineering and security engineering.

## [edit] Legal issues involving cryptography

### [edit] Prohibitions

Cryptography has long been of interest to intelligence gathering agencies and law enforcement agencies. 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 possible widespread access to high quality cryptography.

In some countries, even the domestic use of cryptography is, or has been, restricted. Until 1999, France significantly restricted the use of cryptography domestically. 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, Venezuela, and Vietnam.

^{[31]}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. 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 classified as a munition.

^{[32]}Until the advent of the personal computer and the Internet, this was not especially problematic. Good cryptography is indistinguishable from bad cryptography for nearly all users, and in any case, most of the cryptographic techniques generally available were slow and error prone whether good or bad. 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.### [edit] Export Controls

^{[33]}

^{[34]}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 which 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.

^{[35]}

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.

^{[36]}Cryptography exports from the US are now much less strictly regulated than in the past as a consequence of a major relaxation in 2000;^{[31]}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 (ie, 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.### [edit] NSA involvement

*See also: Clipper chip*

^{[37]}DES was designed to be resistant to differential cryptanalysis,

^{[38]}a powerful and general cryptanalytic technique known to NSA and IBM, that became publicly known only when it was rediscovered in the late 1980s.

^{[39]}According to Steven Levy, IBM rediscovered differential cryptanalysis,

^{[40]}but kept the technique secret at NSA's request. The technique became publicly known only when Biham and Shamir re-rediscovered 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 classified (the cipher, called Skipjack, was declassified in 1998 long after the Clipper initiative lapsed), which 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.

^{[34]}### [edit] Digital Rights Management

*Main Article: Digital Rights Management*

^{[41]}This had a very serious potential impact on the cryptography research community since an argument can be made that

*any*cryptanalytic research violated, or might violate, the DMCA. The FBI and the Justice Department 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 stated that he will not release some 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. Similar statutes have since been enacted in several countries. See for instance the EU Copyright Directive. In 2007, the cryptographic keys responsible for DVD and HDDVD 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.

## [edit] See also

- Topics in cryptography
- List of cryptographers
- Category:Cryptographers
- Books on cryptography
- List of important publications in computer science#Cryptography
- List of open problems in computer science#Cryptography
- International Association for Cryptologic Research
- David Kahn#The Codebreakers
- The Code Book
- Crypto: How the Code Rebels Beat the Government Saving Privacy in the Digital Age
- Applied Cryptography

## [edit] References

- ^
^{a}^{b}^{c}^{d}David Kahn, The Codebreakers, 1967, ISBN 0-684-83130-9. - ^
^{a}^{b}^{c}Oded Goldreich,*Foundations of Cryptography, Volume 1: Basic Tools*, Cambridge University Press, 2001, ISBN 0-521-79172-3 **^**Eerdmans Commentary on the Bible, James D G Dunn, John W Rogerson, eds., Wm. B. Eerdmans Publishing, 2003, ISBN 0-8028-3711-5**^***Kama Sutra*, Sir Richard F. Burton, translator, Part I, Chapter III, 44th and 45th arts.**^**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.- ^
^{a}^{b}^{c}Whitfield Diffie and Martin Hellman, "New Directions in Cryptography", IEEE Transactions on Information Theory, vol. IT-22, Nov. 1976, pp: 644–654. (pdf) - ^
^{a}^{b}^{c}^{d}^{e}^{f}AJ Menezes, PC van Oorschot, and SA Vanstone, Handbook of Applied Cryptography ISBN 0-8493-8523-7. **^**FIPS PUB 197: The official Advanced Encryption Standard.**^**NCUA letter to credit unions, July 2004**^**RFC 2440 - Open PGP Message Format**^**SSH at windowsecurity.com by Pawel Golen, July 2004- ^
^{a}^{b}Bruce Schneier,*Applied Cryptography*, 2nd edition, Wiley, 1996, ISBN 0-471-11709-9. **^**Whitfield Diffie and Martin Hellman, "Multi-user cryptographic techniques" [Diffie and Hellman, AFIPS Proceedings 45, pp109–112, June 8, 1976].**^**Ralph Merkle was working on similar ideas at the time, and Hellman has suggested that the term used should be Diffie-Hellman-Merkle aysmmetric key cryptography.**^**David Kahn, "Cryptology Goes Public", 58*Foreign Affairs*141, 151 (fall 1979), p. 153.**^**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**^**Clifford Cocks. A Note on 'Non-Secret Encryption', CESG Research Report, 20 November 1973.**^**"Shannon": Claude Shannon and Warren Weaver, "The Mathematical Theory of Communication", University of Illinois Press, 1963, ISBN 0-252-72548-4**^**Pascal Junod, "On the Complexity of Matsui's Attack", SAC 2001.**^**Dawn Song, David Wagner, and Xuqing Tian, "Timing Analysis of Keystrokes and Timing Attacks on SSH", In Tenth USENIX Security Symposium, 2001.**^**J. Håstad, R. Impagliazzo, L.A. Levin, and M. Luby, "A Pseudorandom Generator From Any One-Way Function", SIAM J. Computing, vol. 28 num. 4, pp 1364–1396, 1999.**^**László Babai. "Trading group theory for randomness".*Proceedings of the Seventeenth Annual Symposium on the Theory of Computing*, ACM, 1985.**^**G. 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.**^**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.**^**S. Brands, "Untraceable Off-line Cash in Wallets with Observers", In*Advances in Cryptology — Proceedings of CRYPTO*, Springer-Verlag, 1994.**^**R. Canetti, "Universally composable security: a new paradigm for cryptographic protocols", In*Proceedings of the 42nd annual Symposium on the Foundations of Computer Science*(FOCS), pp. 136–154, IEEE, 2001.**^**D. Dolev and A. Yao, "On the security of public key protocols",*IEEE transactions on information theory*, vol. 29 num. 2, pp. 198–208, IEEE, 1983.**^**M. Abadi and P. Rogaway, "Reconciling two views of cryptography (the computational soundness of formal encryption)." In*IFIP International Conference on Theoretical Computer Science (IFIP TCS 2000)*, Springer-Verlag, 2000.**^**D. Song, "Athena, an automatic checker for security protocol analysis", In*Proceedings of the 12th IEEE Computer Security Foundations Workshop (CSFW)*, IEEE, 1999.- ^
^{a}^{b}RSA Laboratories' Frequently Asked Questions About Today's Cryptography **^**Cryptography & Speech from Cyberlaw**^**"Case Closed on Zimmermann PGP Investigation", press note from the IEEE.- ^
^{a}^{b}Levy, Steven (2001).*"Crypto: How the Code Rebels Beat the Government — Saving Privacy in the Digital Age*. Penguin Books, 56. ISBN 0-14-024432-8. **^**Bernstein v USDOJ, 9th Circuit court of appeals decision.**^**The Wassenaar Arrangement on Export Controls for Conventional Arms and Dual-Use Goods and Technologies**^**"The Data Encryption Standard (DES)" from Bruce Schneier's CryptoGram newsletter, June 15, 2000**^**Coppersmith, D. (May 1994). "The Data Encryption Standard (DES) and its strength against attacks" (PDF).*IBM Journal of Research and Development***38**(3): 243.**^**E. Biham and A. Shamir, "Differential cryptanalysis of DES-like cryptosystems", Journal of Cryptology, vol. 4 num. 1, pp. 3–72, Springer-Verlag, 1991.**^**Levy, pg. 56**^**Digital Millennium Copyright Act

## [edit] Further reading

- 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.
*Introduction to Modern Cryptography*by Phillip Rogaway and Mihir Bellare, a mathematical introduction to theoretical cryptography including reduction-based security proofs. PDF download.*Stealing Secrets, Telling Lies: How Spies and Codebreakers Helped Shape the Twentieth Century*, by James Gannon.- Cryptonomicon by Neal Stephenson (novel, WW2 Enigma cryptanalysis figures into the story, though not always realistically).
*Alvin's Secret Code*by Clifford B. Hicks (children's novel that introduces some basic cryptography and cryptanalysis).*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.*Cryptography and Mathematics*by Bernhard Esslinger, 200 pages, part of the free open-source package Cryptool, http://www.cryptool.com.- Ibrahim A. Al-Kadi ,"The origins of cryptology: The Arab contributions”, Cryptologia, 16(2) (April 1992) pp. 97–126.
- Andreas Pfitzmann: Security in IT Networks: Multilateral Security in Distributed and by Distributed Systems

## [edit] External links

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At Wikiversity you can learn more and teach others about

**Cryptography**at:- 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.
- Cryptography: The Ancient Art of Secret Messages by Monica Pawlan - February 1998
- sci.crypt mini-FAQ
- NSA's CryptoKids.
- RSA Laboratories' Frequently Asked Questions About Today's Cryptography

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