Information On cryptography

Image:Lorenz-SZ42-2.jpg Lorenz cipher machine, used in World War II to encrypt very-high-level general staff messages]] Cryptography (or cryptology from Ancient Greek kryptos "hidden, secret"; and gráph "writing", or [[-logy|-logia]] respectively)Liddell and Scotts 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 automated teller machine password and electronic commerce Cryptology prior to the modern age was almost synonymous with [[encryption]] the conversion of information from a readable state to nonsense The sender retained the ability to decrypt the information and therefore avoid unwanted persons being able to read it. Since WWI and the advent of the computer, the methods used to carry out cryptology have become increasingly complex and its application more widespread. Alongside the advancement in cryptology-related technology, the practice has raised a number of legal issues, some of which remain unresolved.

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 algorithm that 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 (cryptography)|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 useless (or even counter-productive) 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 (cryptography) is often used to mean any method of encryption or concealment of meaning. However, in cryptography, codehas 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, wallaby 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 computer . Cryptanalysis is the term used for the study of methods for obtaining the meaning of encrypted information without access to the key normally required to do so; i.e., it is the study of how to crack encryption algorithms or their implementations. Some use the terms cryptographyand cryptologyinterchangeably in English, while others (including US military practice generally) use cryptographyto refer specifically to the use and practice of cryptographic techniques and cryptologyto refer to the combined study of cryptography and cryptanalysis.Oded Goldreich Foundations of Cryptography, Volume 1: Basic Tools Cambridge University Press, 2001, ISBN 0-521-79172-3lt;/ref> 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 information 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 spy military leaders, and diplomat . In recent decades, the field has expanded beyond confidentiality concerns to include techniques for message integrity checking, sender/receiver identity authentication digital signature , Interactive proof system and secure multiparty computation among others.

Classic cryptography

Image:Skytala&EmptyStrip-Shaded.png [[scytale]](rhymes with "Italy"), an early cipher device]] 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 cipher , which rearrange the order of letters in a message (e.g., hello world becomes ehlol owrdl in a trivially simple rearrangement scheme), and substitution cipher , 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. The Ancient Greece are said to have known of ciphers (e.g., the scytale transposition cipher claimed to have been used by the Sparta military).V. V. I︠A︡shchenko (2002). "[http://books.google.com/books?id=cH-NGrpcIMcC&pg=PA6&dq&hl=en#v=onepage&q=&f=false Cryptography: an introduction]. AMS Bookstore. p.6. ISBN 0-8218-2986-6 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 slaves shaved head—under the regrown hair.David Kahn (writer) [[The Codebreakers]] 1967, ISBN 0-684-83130-9. Another Greek method was developed by Polybius (now called the "Polybius#Cryptography ).http://all.net/books/ip/Chap2-1.html A Short History of Cryptography, Fred Cohen 1995, retrieved 8 June 2010] More modern examples of steganography include the use of invisible ink microdot , and digital watermark to conceal information. Ciphertexts produced by a classical cipher (and some modern ciphers) always reveal statistical information about the plaintext, which can often be used to break them. After the discovery of frequency analysis (cryptanalysis) perhaps by the mathematics in medieval Islam 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 puzzle (see cryptogram . Al-Kindi wrote a book on cryptography entitled Risalah fi Istikhraj al-Muamma (Manuscript for the Deciphering Cryptographic Messages, in which described the first cryptanalysis techniques, including some for polyalphabetic cipher .Simon Singh, The Code Book pp. 14-20Ibrahim A. Al-Kadi (April 1992), "The origins of cryptology: The Arab contributions”, [[Cryptologia]]16 (2): 97–126 File:16th century French cypher machine in the shape of a book with arms of Henri II.jpg cipher machine, with arms of Henri II of France ] File:Encoded letter of Gabriel Luetz d Aramon after 1546 with partial deciphering.jpg French Ambassador to the Ottoman Empire after 1546, with partial decipherment]] Essentially all ciphers remained vulnerable to cryptanalysis using the frequency analysis 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 already known to Al-Kindi. Albertis 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 Alberti Cipher Disk 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 Charles 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 cryptanalytically uninformed. It was finally explicitly recognized in the 19th century that secrecy of a ciphers 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 Shannons Maxim—the enemy knows the system. Different 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 grille (cryptography) which was also used for a kind of steganography. With the invention of polyalphabetic ciphers came more sophisticated aids such as Albertis own cipher disk Johannes Trithemius tabula recta scheme, and Thomas Jefferson s Jefferson disk (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 machine —famously including the Enigma machine used by the German government and military from the late 20s and during World War II lt;/ref> 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 [[Espionage|Spies]] and [[Cryptology|Codebreakers]] Helped Shape the Twentieth Century Washington, D.C., Brasseys, 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 numeral system 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, such as 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. Image:Smartcard3.png with smart card capabilities. The 3-by-5-mm chip embedded in the card is shown, enlarged. Smart cards combine low cost and portability with the power to compute cryptographic algorithms.]] Extensive open academic research into cryptography is relatively recent; it began only in the mid-1970s. In recent times, IBM personnel designed the algorithm that became the Federal (i.e., US) Data Encryption Standard Whitfield Diffie and Martin Hellman published Diffie-Hellman Whitfield Diffie and Martin Hellman "New Directions in Cryptography , IEEE Transactions on Information Theory, vol. IT-22, Nov. 1976, pp: 644–654. (http://citeseer.ist.psu.edu/rd/86197922%2C340126%2C1%2C0.25%2CDownload/http://citeseer.ist.psu.edu/cache/papers/cs/16749/http:zSzzSzwww.cs.rutgers.eduzSz%7EtdnguyenzSzclasseszSzcs671zSzpresentationszSzArvind-NEWDIRS.pdf/diffie76new.pdf 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 network , and computer security generally. Some modern cryptographic techniques can only keep their keys secret if certain mathematical problems are intractable, such as the integer factorization 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 ifsome 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 attack , thus when specifying key length , 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, http://web.archive.org/web/20050307081354/www.cacr.math.uwaterloo.ca/hac/ Handbook of Applied Cryptography] ISBN 0-8493-8523-7. Essentially, prior to the early 20th century, cryptography was chiefly concerned with language and lexicographic code patterns. Since then the emphasis has shifted, and cryptography now makes extensive use of mathematics, including aspects of information theory computational complexity theory 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 (e.g., 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. Image:International Data Encryption Algorithm InfoBox Diagram.svg d International Data Encryption Algorithm cipher, used in some versions of Pretty Good Privacy for high-speed encryption of, for instance, electronic mail ] 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 Albertis 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 block cipher 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 DESs designation was finally withdrawn after the AES was adopted).http://www.csrc.nist.gov/publications/fips/fips197/fips-197.pdf 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 encryptionhttp://www.ncua.gov/letters/2004/04-CU-09.pdf NCUA letter to credit unions], July 2004 to e-mail privacy lt;ref name"opgp">RFC 2440 - Open PGP Message Format and Secure Shell http://www.windowsecurity.com/articles/SSH.html 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 function 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 isnt 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 NISTs overall hash algorithm toolkit."http://csrc.nist.gov/groups/ST/hash/documents/FR_Notice_Nov07.pdf National Institute of Standards and Technology] Thus, a NIST hash function competition is underway and meant to select a new U.S. national standard, to be called SHA-3 by 2012. Message authentication code (MACs) are much like cryptographic hash functions, except that a secret key can be used to authenticate the hash value upon 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 (algebra) 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 does not already exist between them, also presents a chicken-and-egg problem which is a considerable practical obstacle for cryptography users in the real world. Image:Diffie and Hellman.jpg and Martin Hellman authors of the first published paper on public-key cryptography]] 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 publickey and a privatekey.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 (writer) 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 keyis typically used for encryption, while the privateor secret keyis 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.Ronald L. Rivest A. Shamir, L. Adleman. http://theory.lcs.mit.edu/~rivest/rsapaper.pdf 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 United Kingdom 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).http://www.fi.muni.cz/usr/matyas/lecture/paper2.pdf 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 cryptography See :Category:Asymmetric-key cryptosystems Image:Firefox-SSL-padlock.png Web browser meant to indicate a page has been sent in SSL or TLS-encrypted protected form. However, such an icon is not a guarantee of security; any subverted browser might mislead a user by displaying such an icon when a transmission is not actually being protected by SSL or TLS.]] 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 forgery 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 Digital Signature Algorithm are two of the most popular digital signature schemes. Digital signatures are central to the operation of public key infrastructure and many network security schemes (e.g., Transport Layer Security many VPN , etc.). Public-key algorithms are most often based on the computational complexity theory 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 curve . Because of the difficulty of the underlying problems, most public-key algorithms involve operations such as modular arithmetic 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 cryptosystem , 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

Image:Enigma.jpg used by Germanys military and civil authorities from the late 1920s through World War II implemented a complex electro-mechanical polyalphabetic cipher Cryptanalysis of the Enigma at Polands Biuro Szyfrów for 7 years before the war, and subsequent decryption at Bletchley Park was important to Allied victory.]] The goal of cryptanalysis is to find some weakness or insecurity in a cryptographic scheme, thus permitting its subversion or evasion. It is a common 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 Statistical randomness 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 exponential time dependent on the key size, as compared to the effort needed to usethe cipher. In such cases, effective security could be achieved if it is proven that the effort required (i.e., "work factor", in Shannons 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 (cryptanalysis) used by the British during WWII. Finally, in a chosen-ciphertext attack the cryptanalyst may be able to chooseciphertexts and learn their corresponding plaintexts. Also important, often overwhelmingly so, are mistakes (generally in the design or use of one of the cryptographic protocol involved; see Cryptanalysis of the Enigma for some historical examples of this). Image:2008-09 Kaiserschloss Kryptologen.JPG monument (center to Polish cryptologists whose breaking of Germany s Enigma machine ciphers, beginning in 1932, altered the course of World War II]] 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, http://citeseer.ist.psu.edu/cache/papers/cs/22094/http:zSzzSzeprint.iacr.orgzSz2001zSz056.pdf/junod01complexity.pdf "On the Complexity of Matsuis 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 (i.e., in a practical time). For instance, the best known algorithms for solving the elliptic curve cryptography 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 attack]]s If a cryptanalyst has access to, for example, 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 A. Wagner and Xuqing Tian, http://citeseer.ist.psu.edu/cache/papers/cs/22094/http:zSzzSzeprint.iacr.orgzSz2001zSz056.pdf/junod01complexity.pdf "Timing Analysis of Keystrokes and Timing Attacks on SSH"], In Tenth USENIX Annual Technical Conference 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 (security) 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 primitive 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 cryptosystemsor cryptographic protocols which guarantee one or more high-level security properties. Note however, that the distinction between cryptographic primitivesand 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 function , one-way function , 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. ElGamal encryption are designed to provide particular functionality (e.g. public key encryption) while guaranteeing certain security properties (e.g. Chosen-plaintext attack security in the random oracle model . Cryptosystems use the properties of the underlying cryptographic primitives to support the systems 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 cryptosystems 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 protocol]]s Some widely known cryptosystems include RSA Schnorr signature El-Gamal encryption, Pretty Good Privacy etc. More complex cryptosystems include electronic cash lt;ref>S. Brands, http://scholar.google.com/url?saU&qhttp://ftp.se.kde.org/pub/security/docs/ecash/crypto93.ps.gz "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 system ,László Babai. http://portal.acm.org/citation.cfm?id22192 "Trading group theory for randomness"]. Proceedings of the Seventeenth Annual Symposium on the Theory of Computing ACM, 1985. (like zero-knowledge proof ,Shafi Goldwasser Silvio Micali and Charles Rackoff "The Knowledge Complexity of Interactive Proof Systems", SIAM J. Computing, vol. 18, num. 1, pp. 186–208, 1989.), systems for secret sharing George 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 (i.e., 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 agency Actually secret communications may be criminal or even treason us; 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 People's Republic of 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 Singapore Tunisia and Vietnam http://www.rsasecurity.com/rsalabs/node.asp?id2152 RSA Laboratories Frequently Asked Questions About Todays 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 http://web.archive.org/web/20051201184530/http://www.cyberlaw.com/cylw1095.html Cryptography & Speech] from Cyberlaw Until the development of the personal computer asymmetric key algorithms (i.e., 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 Federal Bureau of Investigation for several years. No charges were ever filed, however.http://www.ieee-security.org/Cipher/Newsbriefs/1996/960214.zimmerman.html "Case Closed on Zimmermann PGP Investigation"], press note from the IEEE lt;/ref> 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 1st Amendment 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 freedom of speech by the United States Constitution.http://www.epic.org/crypto/export_controls/bernstein_decision_9_cir.html 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.http://www.wassenaar.org/guidelines/index.html 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-Export of cryptography 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 browser 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 Post Office Protocol servers via TLS, and can send and receive email encrypted with S/MIME Many Internet users dont realize that their basic application software contains such extensive cryptosystem . These browsers and email programs are so ubiquitous that even governments whose intent is to regulate civilian use of cryptography generally dont 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 Data Encryption Standard during its development at IBM and its consideration by the National Bureau of Standards as a possible Federal Standard for cryptography.http://www.schneier.com/crypto-gram-0006.html#DES "The Data Encryption Standard (DES)"] from Bruce Schneier s CryptoGram newsletter, June 15, 2000 DES was designed to be resistant to differential cryptanalysis lt;/ref> a powerful and general cryptanalytic technique known to NSA and IBM, that became publicly known only when it was rediscovered in the late 1980s.Eli Biham and A. Shamir, http://scholar.google.com/url?saU&qhttp://www.springerlink.com/index/K54H077NP8714058.pdf "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 NSAs 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 NSAs involvement was the 1993 Clipper chip affair, an encryption microchip intended to be part of the Capstone (cryptography) cryptography-control initiative. Clipper was widely criticized by cryptographers for two reasons. The cipher algorithm was then classified (the cipher, called Skipjack (cipher) 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 key escrow 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 copyright d 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.http://www.copyright.gov/legislation/dmca.pdf Digital Millennium Copyright Act] This had a noticeable impact on the cryptography research community since an argument can be made that anycryptanalytic research violated, or might violate, the DMCA. Similar statutes have since been enacted in several countries and regions, including the implementation in the Directive on the harmonization of certain aspects of copyright and related rights in the information society Similar restrictions are called for by treaties signed by World Intellectual Property Organization member-states. The United States Department of Justice and Federal Bureau of Investigation have not enforced the DMCA as rigorously as had been feared by some, but the law, nonetheless, remains a controversial one. Niels Ferguson a well-respected cryptography researcher, has publicly statedhttp://www.macfergus.com/niels/dmca/cia.html that he will not release some of his research into an Intel Corporation security design for fear of prosecution under the DMCA. 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 five months pending trial for alleged violations of the DMCA arising from work he done in Russia, where the work was legal. In 2007, the cryptographic keys responsible for Blu-ray and HD DVD content scrambling were AACS encryption key controversy onto the Internet In both cases, the MPAA sent out numerous DMCA takedown notices, and there was a massive internet backlash triggered by the perceived impact of such notices on fair use and free speech

References

External links

* * http://ciphersbyritter.com/GLOSSARY.HTM Crypto Glossary and Dictionary of Technical Cryptography] * http://www.attackprevention.com/Cryptology/ Attack/Prevention] Resource for Cryptography Whitepapers, Tools, Videos, and Podcasts. * http://www.pawlan.com/Monica/crypto/ Cryptography: The Ancient Art of Secret Messages] by Monica Pawlan - February 1998 * http://www.cacr.math.uwaterloo.ca/hac/ Handbook of Applied Cryptography] by A. J. Menezes, P. C. van Oorschot, and S. A. Vanstone (PDF download available), somewhat more mathematical than Schneiers book. * http://www.nsa.gov/kids/ NSAs CryptoKids]. * http://www.cryptool.org/download/CrypToolPresentation-en.pdf Overview and Applications of Cryptology] by the CrypTool Team; PDF; 3.8 MB—July 2008 * http://www.rsasecurity.com/rsalabs/node.asp?id2152 RSA Laboratories frequently asked questions about today cryptography] * [http://www.spinstop.com/schlafly/crypto/faq.htm sci.crypt mini-FAQ] * [http://wiki.crypto.rub.de/Buch/slides_movies.php Slides of a two-semester course ntroduction to Cryptography] by Prof. Christof Paar, University of Bochum (slides are in English, site contains also videos in German) * [http://www.baconscipher.com/EarlyCryptology.html Early Cryptology, Cryptographic Shakespeare] * [http://www2.warwick.ac.uk/fac/soc/pais/staff/aldrich/vigilant/lectures/gchq GCHQ: Britains Most Secret Intelligence Agency] * [http://www.rbcafe.com/Cryptix Cryptix, complete cryptography solution for Mac OS X.] {{Featured article}} {{Crypto navbox}} {{espionage}} {{Hidden messages}} {{intelligence cycle management}} [[Category:Cryptography| ]] [[Category:Formal sciences]] [[Category:Mathematical science occupations]] [[Category:Banking technology]] {{Link FA|he}} [[af:Kriptografie]] [[ar:علم التعمية]] [[bn:তথ্যগুপ্তিবিদ্যা]] [[be-x-old:Крыптаграфія]] [[bg:Криптография]] [[ca:Criptografia]] [[cs:Kryptografie]] [[da:Kryptografi]] [[de:Kryptographie]] [[nv:Cryptographic]] [[et:Krüptograafia]] [[el:Κρυπτογραφία]] [[es:Criptografía]] [[eu:Kriptografia]] [[fa:رمزنگاری]] [[fr:Cryptographie]] [[gl:Criptografía]] [[gan:暗號學]] [[ko:암호학]] [[hi:बीज-लेखन]] [[hr:Kriptografija]] [[id:Kriptografi]] [[it:Crittografia]] [[he:קריפטוגרפיה]] [[ka:კრიპტოგრაფია]] [[kk:Криптография]] [[la:Cryptographia]] [[lv:Kriptogrāfija]] [[hu:Kriptográfia]] [[ml:ഗൂഢശാസ്ത്രം]] [[ms:Kriptografi]] [[mn:Криптограф]] [[nl:Cryptografie]] [[ja:暗号理論]] [[no:Kryptografi]] [[nn:Kryptografi]] [[mhr:Криптографий]] [[uz:Kriptografiya]] [[pms:Criptografìa]] [[pt:Criptografia]] [[ro:Criptografie]] [[ru:Криптография]] [[sq:Kriptografia]] [[scn:Crittugrafìa]] [[sl:Kriptografija]] [[sr:Криптографија]] [[fi:Salaus]] [[sv:Kryptografi]] [[ta:மறையீட்டியல்]] [[th:วิทยาการเข้ารหัสลับ]] [[tg:Криптография]] [[tr:Kriptografi]] [[uk:Криптографія]] [[ur:Cryptography]] [[vi:Mật mã học]] [[yi:קריפטאגראפיע]] [[zh:密码学]]
System.IndexOutOfRangeException: Index was outside the bounds of the array. at _Default.parseWiki(String inContent)
at _Default.parseWiki(String inContent)

Search This Site

Take Earn Money Tour
Here you will learn how you can earn good money from Reach Information Portal. We are creating a take an online tour for earning money for making you people understand things better.

More Information Services
Translate This Article:

Ask Experts Suggestions
Have some queries about this content ? Feel free to participate in Experts Forum and Earn money for points earned.

Read AskE

RSS Feed · About Us · Site Statitics Info · Contact Us · Content Sharing Policy · Terms and Conditions ·
© Copyright 2008 Reach Information