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Encyclopedia > Cryptography
The German Lorenz cipher machine, used in World War II for encryption of very high-level general staff messages
The German Lorenz cipher machine, used in World War II for encryption of very high-level general staff messages

Cryptography (or cryptology; derived from Greek κρυπτός kryptós "hidden," and the verb γράφω gráfo "write" or λεγειν legein "to speak") is the study of message secrecy. 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. 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. Download high resolution version (1141x848, 146 KB)A Lorenz SZ42 cipher machine on display at Bletchley Park museum. ... Download high resolution version (1141x848, 146 KB)A Lorenz SZ42 cipher machine on display at Bletchley Park museum. ... For the fish, see Tuna. ... Combatants Allied powers: China France Great Britain Soviet Union United States and others Axis powers: Germany Italy Japan and others Commanders Chiang Kai-shek Charles de Gaulle Winston Churchill Joseph Stalin Franklin Roosevelt Adolf Hitler Benito Mussolini Hideki Tōjō Casualties Military dead: 17,000,000 Civilian dead: 33,000... Cryptology is an umbrella term for cryptography and cryptanalysis. ... Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... Computer science, or computing science, is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ... A bundle of optical fiber. ... This article describes how security can be achieved through design and engineering. ... Engineering is the design, analysis, and/or construction of works for practical purposes. ... An NCR Personas 85-Series interior, multi-function ATM in the USA Smaller indoor ATMs dispense money inside convenience stores and other busy areas, such as this off-premise Wincor Nixdorf mono-function ATM in Sweden. ... A password is a form of secret authentication data that is used to control access to a resource. ... This article does not cite any references or sources. ...

Contents

Terminology

Until modern times, cryptography referred almost exclusively to encryption, the process of converting ordinary information (plaintext) into unintelligible gibberish (ie, ciphertext). 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 so rather 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. “Cipher” redirects here. ... In cryptography, plaintext is information used as input to an encryption algorithm; the output is termed ciphertext. ... In cryptography, plaintext is information used as input to an encryption algorithm; the output is termed ciphertext. ... This article is about algorithms for encryption and decryption. ... In mathematics, computing, linguistics, and related disciplines, an algorithm is a finite list of well-defined instructions for accomplishing some task that, given an initial state, will terminate in a defined end-state. ... A key is a piece of information that controls the operation of a cryptography algorithm. ...


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. A colloquialism is an informal expression, that is, an expression not used in formal speech or writing. ... In the context of cryptography, a code is a method used to transform a message into an obscured form, preventing those not in on the secret from understanding what is actually transmitted. ... A Code word may refer any of several concepts: For telecommunications senses, see Code word (telecommunication). ...


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. In this respect, English usage is more tolerant of overlapping meanings and word origins than are several European languages in which meanings of cognate words are more restricted.


History of cryptography and cryptanalysis

The Ancient Greek scytale (rhymes with Italy), probably much like this modern reconstruction, may have been one of the earliest devices used to implement a cipher.
The Ancient Greek scytale (rhymes with Italy), probably much like this modern reconstruction, may have been one of the earliest devices used to implement a cipher.
Main article: History of cryptography

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). 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, amongst others. Wikipedia does not have an article with this exact name. ... Wikipedia does not have an article with this exact name. ... This article is about the encryption device; for the Dune character, see Scytale (Dune). ... The history of cryptography dates back thousands of years. ... The ASCII codes for the word Wikipedia represented in binary, the numeral system most commonly used for encoding computer information. ... Authentication (from Greek αυθεντικός; real or genuine, from authentes; author) is the act of establishing or confirming something (or someone) as authentic, that is, that claims made by or about the thing are true. ... In cryptography, a digital signature or digital signature scheme is a type of asymmetric cryptography used to simulate the security properties of a signature in digital, rather than written, form. ... For interactive proof, see interactive proof system or interactive theorem proving. ... In cryptography, secure multiparty computation is a problem that was initially suggested by Andrew C. Yao in a 1982 paper. ...


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. In classical cryptography, a transposition cipher changes one character from the plaintext to another (to decrypt the reverse is done). ... In cryptography, a substitution cipher is a method of encryption by which units of plaintext are substituted with ciphertext according to a regular system; the units may be single letters (the most common), pairs of letters, triplets of letters, mixtures of the above, and so forth. ... The action of a Caesar cipher is to replace each plaintext letter with one a fixed number of places down the alphabet. ... Gaius Julius Caesar [1] (Latin pronunciation ; English pronunciation ; July 12 or July 13, 100 BC or 102 BC – March 15, 44 BC), was a Roman military and political leader and one of the most influential men of World history. ...


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.[1] 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.[2] 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.[3] More modern examples of steganography include the use of invisible ink, microdots, and digital watermarks to conceal information. Secrecy is the practice of sharing information among a group of people, which can be as small as one person, while hiding it from others. ... SPY may refer to: SPY (spiders), ticker symbol for Standard & Poors Depository Receipts SPY (magazine), a satirical monthly, trademarked all-caps SPY (Ivory Coast), airport code for San Pédro, Côte dIvoire SPY (Ship Planning Yard), a U.S. Navy acronym SPY, short for MOWAG SPY, a... This page is about negotiations; for the board game, see Diplomacy (game). ... 666 is the natural number following 665 and preceding 667. ... The Number of the Beast is a concept from the Book of Revelation of the New Testament of the Christian Bible. ... Topics in Christianity Movements · Denominations Ecumenism · Preaching · Prayer Music · Liturgy · Calendar Symbols · Art · Criticism Important figures Apostle Paul · Church Fathers Constantine · Athanasius · Augustine Anselm · Aquinas · Palamas · Wycliffe Tyndale · Luther · Calvin · Wesley Arius · Marcion of Sinope Pope · Archbishop of Canterbury Patriarch of Constantinople Christianity Portal This box:      A Christian () is a... This article is about the Christian scriptures. ... Visions of John of Patmos, as depicted in the Très Riches Heures du Duc de Berry. ... Nero[1] Claudius Caesar Augustus Germanicus (December 15, 37 – June 9, 68)[2], born Lucius Domitius Ahenobarbus, also called Nero Claudius Caesar Drusus Germanicus, was the fifth and last Roman Emperor of the Julio-Claudian dynasty. ... Kamasutram, generally known to the Western world as Kama Sutra, is an ancient Indian text widely considered to be the standard work on love in Sanskrit literature. ... Steganography is the art and science of writing hidden messages in such a way that no one apart from the intended recipient knows of the existence of the message; this is in contrast to cryptography, where the existence of the message itself is not disguised, but the content is obscured. ... This article does not cite any references or sources. ... Invisible ink is a substance used for writing, which is either invisible on application, or soon thereafter, and which later on can be made visible by some means. ... HI Mark IV microdot camera A microdot is a text or image shrunk to prevent viewing by unintended recipients. ... Digital watermarking is a technique which allows to add hidden copyright or other verification messages to digital audio, video, or image signals and documents. ...


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 Arab discovery of frequency analysis (ca 1000CE), 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 (there is some indication of early Arab knowledge of them). Alberti's innovation was to use different ciphers (i.e., substitution alphabets) for various parts of a message (often each successive plaintext letter). 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.[3] In mathematics, physics and signal processing, frequency analysis is a method to decompose a function, wave, or signal into its frequency components so that it is possible to have the frequency spectrum. ... A puzzle is a problem or enigma that challenges ingenuity. ... For the plants which reproduce by using spores, see Cryptogam. ... A polyalphabetic cipher is any cipher based on substitution, using multiple substitution alphabets. ... Leone Battista Alberti (February 1404 - 25th April 1472), Italian painter, poet, linguist, philosopher, cryptographer, musician, architect, and general Renaissance polymath . ... The Vigenère cipher is named for Blaise de Vigenère (pictured), although Giovan Batista Belaso had invented the cipher earlier. ... Charles Babbage FRS (26 December 1791 – 18 October 1871) was an English mathematician, philosopher, mechanical engineer and (proto-) computer scientist who originated the idea of a programmable computer. ...

The Enigma machine, used in several variants by the German military between the late 1920s and the end of World War II, implemented a complex electro-mechanical polyalphabetic cipher to protect sensitive communications. Breaking the Enigma cipher at the Biuro Szyfrów, and the subsequent large-scale decryption of Enigma traffic at Bletchley Park, was an important factor contributing to the Allied victory in WWII.
The Enigma machine, used in several variants by the German military between the late 1920s and the end of World War II, implemented a complex electro-mechanical polyalphabetic cipher to protect sensitive communications. Breaking the Enigma cipher at the Biuro Szyfrów, and the subsequent large-scale decryption of Enigma traffic at Bletchley Park, was an important factor contributing to the Allied victory in WWII.[3]

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 recognized in the 19th century that secrecy of a cipher's algorithm is not a sensible or practical safeguard; in fact, any adequate cryptographic scheme (including ciphers) should remain secure even if the adversary knows the cipher algorithm itself. Secrecy of the key should alone be sufficient for confidentiality when under attack — for good ciphers. 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'. Enigma This is a screenshot of a copyrighted computer game or video game. ... Enigma This is a screenshot of a copyrighted computer game or video game. ... The plugboard, keyboard, lamps and finger-wheels of the rotors emerging from the inner lid of a three-rotor German military Enigma machine (version with labels) The Enigma machine was a cipher machine used to encrypt and decrypt secret messages. ... Combatants Allied powers: China France Great Britain Soviet Union United States and others Axis powers: Germany Italy Japan and others Commanders Chiang Kai-shek Charles de Gaulle Winston Churchill Joseph Stalin Franklin Roosevelt Adolf Hitler Benito Mussolini Hideki Tōjō Casualties Military dead: 17,000,000 Civilian dead: 33,000... This article is about algorithms for encryption and decryption. ... This article or section contains information that has not been verified and thus might not be reliable. ... The Biuro Szyfrów ( (?), Polish for Cipher Bureau) was the Polish agency concerned with cryptology between World Wars I and II. The Bureau enjoyed notable successes against Soviet cryptography during the Polish-Soviet War, helping to preserve Polands independence. ... During World War II, codebreakers at Bletchley Park decrypted and interpreted messages from a large number of Axis code and cipher systems, including the German Enigma machine. ... Auguste Kerckhoffs Dr Auguste Kerckhoffs (19 January 1835 - 1903) was a Flemish linguist and cryptographer who was professor of languages at the School of Higher Commercial Studies in Paris in the late 19th century. ... In cryptography, Kerckhoffs principle (also called Kerckhoffs assumption, axiom or law) was stated by Auguste Kerckhoffs in the 19th century: a cryptosystem should be secure even if everything about the system, except the key, is public knowledge. ... Claude Elwood Shannon (April 30, 1916 _ February 24, 2001) has been called the father of information theory, and was the founder of practical digital circuit design theory. ...


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 (invented independently by Bazeries around 1900). Early in the 20th century, several mechanical encryption/decryption devices were invented, 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.[4] This article is about the encryption device; for the Dune character, see Scytale (Dune). ... The Temple to Athena, the Parthenon Ancient Greece is a period in Greek history that lasted for around three thousand years. ... In the history of cryptography, a grille cipher was a technique for encrypting a plaintext by writing it onto a sheet of paper through a pierced sheet (of paper or cardboard or similar). ... A cipher disk is an enciphering and deciphering tool developed in the 15th Century by Leon Battista Alberti. ... Polygraphia (1518) — the first printed book on cryptography. ... Tabula recta In cryptography, the tabula recta is a square table of alphabets, each one made by shifting the previous one to the left. ... Thomas Jefferson (13 April 1743 N.S.–4 July 1826) was the third President of the United States (1801–09), the principal author of the Declaration of Independence (1776), and one of the most influential Founding Fathers for his promotion of the ideals of Republicanism in the United States. ... Étienne Bazeries (21 August 1846 - 7 November 1931) was a French military cryptanalyst active between 1890 and the First World War. ... In cryptography, a rotor machine is a electro-mechanical device used for encrypting and decrypting secret messages. ... The plugboard, keyboard, lamps and finger-wheels of the rotors emerging from the inner lid of a three-rotor German military Enigma machine (version with labels) The Enigma machine was a cipher machine used to encrypt and decrypt secret messages. ... Combatants Allied powers: China France Great Britain Soviet Union United States and others Axis powers: Germany Italy Japan and others Commanders Chiang Kai-shek Charles de Gaulle Winston Churchill Joseph Stalin Franklin Roosevelt Adolf Hitler Benito Mussolini Hideki Tōjō Casualties Military dead: 17,000,000 Civilian dead: 33,000...


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. Electronics is the study of the flow of charge through various materials and devices such as, semiconductors, resistors, inductors, capacitors, nano-structures, and vacuum tubes. ... The binary numeral system, or base-2 number system, is a numeral system that represents numeric values using two symbols, usually 0 and 1. ... This article is about the unit of information. ...

A credit card with smart card capabilities. The 3 by 5 mm chip embedded in the card is shown enlarged in the insert. Smart cards attempt to combine portability with the power to compute modern cryptographic algorithms.

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,[5] 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.[6] 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. Image File history File links Smartcard. ... Image File history File links Smartcard. ... Smart card used for health insurance in France. ... The Data Encryption Standard (DES) is a cipher (a method for encrypting information) selected as an official Federal Information Processing Standard (FIPS) for the United States in 1976, and which has subsequently enjoyed widespread use internationally. ... NBS can stand for: Nash Bargaining Solution in Economics National Banking System in Economics National Bureau of Standards which is, today, called NIST (National Institute of Standards and Technology). ... Diffie-Hellman key exchange is a cryptographic protocol which allows two parties to agree on a secret key over an insecure communication channel. ... In cryptology, RSA is an algorithm for public-key encryption. ... “Computer Networks” redirects here. ... In mathematics, the integer prime-factorization (also known as prime decomposition) problem is this: given a positive integer, write it as a product of prime numbers. ... In mathematics, specifically in abstract algebra and its applications, discrete logarithms are group-theoretic analogues of ordinary logarithms. ... Excerpt from a one-time pad. ...


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] In cryptanalysis, a brute force attack on a cipher is a brute-force search of the key space; that is, testing all possible keys, in an attempt to recover the plaintext used to produce a particular ciphertext. ... In cryptography, the key size (alternatively key length) is a measure of the number of possible keys which can be used in a cipher. ... Molecule of alanine used in NMR implementation of error correction. ...


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). This article does not cite any references or sources. ... A bundle of optical fiber. ... As a branch of the theory of computation in computer science, computational complexity theory describes the scalability of algorithms, and the inherent difficulty in providing scalable algorithms for specific computational problems. ... A graph of a normal bell curve showing statistics used in educational assessment and comparing various grading methods. ... Combinatorics is a branch of pure mathematics concerning the study of discrete (and usually finite) objects. ... Abstract algebra is the field of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. ... Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. ... Engineering is the design, analysis, and/or construction of works for practical purposes. ... This article is an overview of cryptographic engineering which notes at least some of the differences between ordinary engineering and the cryptographic sort. ... Security engineering is the field of engineering dealing with the security and integrity of real-world systems. ... Fig. ... Quantum cryptography is an approach based on quantum physics for secure communications. ... Molecule of alanine used in NMR implementation of error correction. ...


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. This article is intended to be an analytic glossary, or alternatively, an organized collection of annotated pointers. ...


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 1976.[5] Symmetric-key algorithms are a class of algorithms for cryptography that use trivially related cryptographic keys for both decryption and encryption. ...

One round (out of 8.5) of the patented IDEA cipher, used in some versions of PGP for high-speed encryption of, for instance, e-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 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. Image File history File links Download high resolution version (640x658, 56 KB)Original diagram for Wikipedia File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links Download high resolution version (640x658, 56 KB)Original diagram for Wikipedia File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... A patent is a set of exclusive rights granted by a state to a patentee for a fixed period of time in exchange for a disclosure of an invention. ... In cryptography, the International Data Encryption Algorithm (IDEA) is a block cipher designed by Xuejia Lai (來學嘉) and James L. Massey of ETH Zurich and was first described in 1991. ... PGP Encryption (Pretty Good Privacy) is a computer program that provides cryptographic privacy and authentication. ... Electronic mail, abbreviated e-mail or email, is a method of composing, sending, and receiving messages over electronic communication systems. ... In cryptography, a block cipher is a type of symmetric key cipher which operates on groups of bits of a fixed length, termed blocks. ... In cryptography, a stream cipher is a cipher in which the input data are encrypted one bit (sometimes one byte) at a time. ... In cryptography, a block cipher operates on blocks of fixed length, often 64 or 128 bits. ...


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] The Data Encryption Standard (DES) is a cipher (a method for encrypting information) selected as an official Federal Information Processing Standard (FIPS) for the United States in 1976, and which has subsequently enjoyed widespread use internationally. ... In cryptography, the Advanced Encryption Standard (AES), also known as Rijndael, is a block cipher adopted as an encryption standard by the U.S. government. ... There are a number of standards related to cryptography. ... In cryptography, Triple DES is a block cipher formed from the Data Encryption Standard (DES) cipher by using it three times. ... The protection of electronic mail from unauthorized access and inspection is known as e-mail privacy. ... In computing, Secure shell, or SSH, is both a computer program and an associated network protocol designed for logging into and executing commands on a remote computer. ...


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] In cryptography, RC4 (also known as ARC4 or ARCFOUR) is the most widely-used software stream cipher and is used in popular protocols such as Secure Sockets Layer (SSL) (to protect Internet traffic) and WEP (to secure wireless networks). ...


Cryptographic hash functions (often called message digest functions) do not 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. In cryptography, a cryptographic hash function is a hash function with certain additional security properties to make it suitable for use as a primitive in various information security applications, such as authentication and message integrity. ... A hash function [1] is a reproducible method of turning some kind of data into a (relatively) small number that may serve as a digital fingerprint of the data. ...


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. A cryptographic message authentication code (MAC) is a short piece of information used to authenticate a message. ...


Public-key cryptography

Symmetric-key cryptosystems typically use the same key for encryption and decryption, though this 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 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. A big random number is used to make a public-key pair. ... In cryptography, key management includes all of the provisions made in a cryptosystem design, in cryptographic protocols in that design, in user procedures, and so on, which are related to generation, exchange, storage, safeguarding, use, vetting, and replacement of keys. ... y=x², for all integer values of 1≤x≤25. ... In cryptography, and particularly in analytic or academic discussions of it, a secure channel is a method or technique assumed to provide means by which data can be transferred from one place or user to another without risk of interception or tampering. ... The chicken or the egg is a reference to the causality dilemma which arises from the expression which came first, the chicken or the egg?. When used in reference to difficult problems, a chicken and egg problem is similar to a Catch 22 situation where something cannot happen until a...

Whitfield Diffie and Martin Hellman, inventors of public-key cryptography
Whitfield Diffie and Martin Hellman, inventors of 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 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] Image File history File links Diffie_and_Hellman. ... Image File history File links Diffie_and_Hellman. ... Whitfield Diffie Bailey Whitfield Whit Diffie (born June 5, 1944) is a US cryptographer and one of the pioneers of public-key cryptography. ... Martin Hellman - Wikipedia, the free encyclopedia /**/ @import /skins-1. ... Whitfield Diffie Bailey Whitfield Whit Diffie (born June 5, 1944) is a US cryptographer and one of the pioneers of public-key cryptography. ... Martin Hellman - Wikipedia, the free encyclopedia /**/ @import /skins-1. ... David Kahn is a US historian, journalist and writer. ...


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.[5] Diffie-Hellman key exchange is a cryptographic protocol which allows two parties to agree on a secret key over an insecure communication channel. ...


In 1978, Ronald Rivest, Adi Shamir, and Len Adleman invented RSA, another public-key system.[16] Professor Ron Rivest Professor Ronald Linn Rivest (born 1947, Schenectady, New York) is a cryptographer, and is the Viterbi Professor of Computer Science at MITs Department of Electrical Engineering and Computer Science. ... Adi Shamir at the CRYPTO 2003 conference. ... Leonard Adleman Leonard Adleman (born December 31, 1945) is a theoretical computer scientist and professor of computer science and molecular biology at the University of Southern California. ... In cryptology, RSA is an algorithm for public-key encryption. ...


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] James H. Ellis (1924–November 1997) was an engineer and mathematician. ... The Government Communications Headquarters (GCHQ) (previously named the Government Code and Cipher School (GC&CS)) is the main British intelligence service providing signals intelligence (SIGINT). ... Malcolm J. Williamson discovered what is now known as Diffie-Hellman key exchange while working at GCHQ. Williamson studied at Manchester Grammar School, winning a Gold prize at the 1968 International Mathematical Olympiad in Moscow. ... Clifford Christopher Cocks is a British mathematician and cryptographer at GCHQ who invented the widely-used encryption algorithm now commonly known as RSA, about three years before it was independently developed by Rivest, Shamir, and Adleman at MIT. He has not been generally recognised for this achievement because his work...


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 cryptology, RSA is an algorithm for public-key encryption. ... The Cramer-Shoup system is an asymmetric key encryption algorithm for public key cryptography, and was the first efficient scheme proven to be secure against adaptive chosen ciphertext attack using standard cryptographic assumptions. ... The ElGamal algorithm is an asymmetric key encryption algorithm for public key cryptography which is based on Diffie-Hellman key agreement. ... Elliptic curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ...

Padlock icon from the Firefox 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; a subverted browser might mislead a user by displaying a proper icon when a transmission is not actually being protected by SSL or TLS.
Padlock icon from the Firefox 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; a subverted browser might mislead a user by displaying a proper 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 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] Image File history File links Firefox-SSL-padlock. ... Image File history File links Firefox-SSL-padlock. ... Firefox may refer to: Firefox (novel), written by Craig Thomas, published in 1978 Firefox (film), the 1982 movie starring Clint Eastwood, based on the novel Firefox (arcade game), the laserdisc arcade game based on the movie Mozilla Firefox, a web browser The Red Fox or the Red Panda, based on... In cryptography, a digital signature or digital signature scheme is a type of asymmetric cryptography used to simulate the security properties of a signature in digital, rather than written, form. ... John Hancocks signature is one of the most prominent on the United States Declaration of Independence. ... Forgery is the process of making or adapting objects or documents (see false document), with the intention to deceive. ... In cryptology, RSA is an algorithm for public-key encryption. ... The Digital Signature Algorithm (DSA) is a United States Federal Government standard or FIPS for digital signatures. ... In cryptography, a public key infrastructure (PKI) is an arrangement that binds public keys with respective user identities by means of a certificate authority (CA). ... This article or section does not adequately cite its references or sources. ... A Virtual Private Network, or VPN, is a private communications network usually used within a company, or by several different companies or organizations, communicating over a public network. ...


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] As a branch of the theory of computation in computer science, computational complexity theory describes the scalability of algorithms, and the inherent difficulty in providing scalable algorithms for specific computational problems. ... Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. ... In number theory, the integer factorization problem is the problem of finding a non-trivial divisor of a composite number; for example, given a number like 91, the challenge is to find a number such as 7 which divides it. ... In mathematics, specifically in abstract algebra and its applications, discrete logarithms are group-theoretic analogues of ordinary logarithms. ... Elliptic curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ... In mathematics, an elliptic curve is a plane curve defined by an equation of the form y2 = x3 + a x + b, which is non-singular; that is, its graph has no cusps or self-intersections. ... Modular arithmetic (sometimes called modulo arithmetic, or clock arithmetic because of its use in the 24-hour clock system) is a system of arithmetic for integers, where numbers wrap around after they reach a certain value — the modulus. ... In cryptography, public-key cryptosystems are convenient in that they do not require the sender and receiver to share a common secret in order to communicate securely (among other useful properties). ...


Cryptanalysis

Main article: Cryptanalysis

The goal of cryptanalysis is to find some weakness or insecurity in a cryptographic scheme, thus permitting its subversion or evasion. Cryptanalysis might be undertaken by a malicious attacker, attempting to subvert a system, or by the system's designer (or others) attempting to evaluate whether a system has vulnerabilities, and so it is not inherently a hostile act. In modern practice, however, cryptographic algorithms and protocols must be carefully examined and tested to offer any assurance of the system's security (at least, under clear — and hopefully reasonable — assumptions). Cryptanalysis (from the Greek kryptós, hidden, and analýein, to loosen or to untie) is the study of methods for obtaining the meaning of encrypted information, without access to the secret information which is normally required to do so. ...


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. Bell Laboratories (also known as Bell Labs and formerly known as AT&T Bell Laboratories and Bell Telephone Laboratories) was the main research and development arm of the United States Bell System. ... Claude Elwood Shannon (April 30, 1916 _ February 24, 2001) has been called the father of information theory, and was the founder of practical digital circuit design theory. ... Excerpt from a one-time pad. ... In statistics a random number is a single observation (outcome) of a specified random variable. ... The EFFs US$250,000 DES cracking machine contained over 1,800 custom chips and could brute force a DES key in a matter of days — the photograph shows a DES Cracker circuit board fitted with several Deep Crack chips. ... In complexity theory, exponential time is the computation time of a problem where the time to complete the computation, m(n), is bounded by an exponential function of the problem size, n (i. ...


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). In cryptography, a ciphertext-only attack is a form of cryptanalysis where the attacker is assumed to have access only to a set of ciphertexts. ... The known-plaintext attack (KPA) is an attack model for cryptanalytic where the attacker has samples of both the plaintext and its encrypted version (ciphertext) and is at liberty to make use of them to reveal further secret information; typically this is the secret key. ... A chosen plaintext attack is any form of cryptanalysis which presumes that the attacker has the capability to choose arbitrary plaintexts to be encrypted and obtain the corresponding ciphertexts. ... In cryptanalysis, gardening was a term used at Bletchley Park during World War II for schemes to entice the Germans to include known plaintext, which they called cribs, in their encrypted messages. ... A chosen-ciphertext attack (CCA) is an attack model for cryptanalysis in which the cryptanalyst chooses a ciphertext and causes it to be decrypted with an unknown key. ... A cryptographic protocol is an abstract or concrete protocol that performs a security-related function and applies cryptographic methods. ... This article or section contains information that has not been verified and thus might not be reliable. ...


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.[19] This is a considerable improvement on brute force attacks. In cryptography, linear cryptanalysis is a general form of cryptanalysis based on finding affine approximations to the action of a cipher. ...


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. In number theory, the integer factorization problem is the problem of finding a non-trivial divisor of a composite number; for example, given a number like 91, the challenge is to find a number such as 7 which divides it. ... In mathematics, specifically in abstract algebra and its applications, discrete logarithms are group-theoretic analogues of ordinary logarithms. ... Elliptic curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ...


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. In cryptography, a side channel attack is any attack based on information gained from the physical implementation of a cryptosystem, rather than weaknesses in the mathematical algorithms (compare cryptanalysis). ... In cryptography, a timing attack is a form of side channel attack where the attacker tries to break a cryptosystem by analyzing the time taken to execute cryptographic algorithms. ... Traffic analysis is the process of intercepting and examining messages in order to deduce information from patterns in communication. ... Social engineering has several meanings: Social engineering (political science) Social engineering (computer security) This is a disambiguation page — a navigational aid which lists pages that might otherwise share the same title. ... Bribery is a crime implying a sum or gift given alters the behaviour of the person in ways not consistent with the duties of that person. ... Extortion is a criminal offense, which occurs when a person either obtains money, property or services from another through coercion or intimidation or threatens one with physical harm unless they are paid money or property. ... For other uses, see Blackmail (disambiguation). ... Spy and Secret agent redirect here. ...


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.[6] Since the P versus NP problem is currently unsolved, we don't know if one-way functions really do exist. More complicated cryptographic tools are then built from these basic primtives. For instance, if one-way functions exist, then secure pseudorandom generators and secure pseudorandom functions exist.[21] A Cryptographic primitives are well-established cryptographic routines that are frequently used in security-related topics. ... Unsolved problems in computer science: Do one-way functions exist? A one-way function is a function that is easy to compute but hard to invert. ... Graph of example function, The mathematical concept of a function expresses the intuitive idea of deterministic dependence between two quantities, one of which is viewed as primary (the independent variable, argument of the function, or its input) and the other as secondary (the value of the function, or output). A... Diagram of complexity classes provided that P ≠ NP. The existence of problems outside both P and NP-complete in this case was established by Ladner. ... A cryptographically secure pseudo-random number generator (CSPRNG) is a pseudo-random number generator (PRNG) with properties that make it suitable for use in cryptography. ...


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 A cryptosystem (or cryptographic system) is the package of all procedures, protocols, cryptographic algorithms and instructions used for encoding and decoding messages using cryptography. ... PGP Encryption (Pretty Good Privacy) is a computer program that provides cryptographic privacy and authentication. ... Secure Shell or SSH is a network protocol that allows data to be exchanged over a secure channel between two computers. ... This article or section does not adequately cite its references or sources. ... This article or section does not adequately cite its references or sources. ... In cryptography, a public key infrastructure (PKI) is an arrangement that binds public keys with respective user identities by means of a certificate authority (CA). ... In cryptography, a digital signature or digital signature scheme is a type of asymmetric cryptography used to simulate the security properties of a signature in digital, rather than written, form. ...


Other cryptographic primitives include the encryption algorithms themselves, one-way permutations, trapdoor permutations, etc. In cryptography, a one-way permutation is a one-way function that is also a permutation, that is, a one-way function that is both injective and surjective. ... A trapdoor function is a function that is easy to compute in one direction, and difficult to compute in the opposite direction (finding its inverse) without special information, called the trapdoor. ...


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. In information technology, backup refers to the copying of data so that these additional copies may be restored after a data loss event. ... A cryptographic protocol is an abstract or concrete protocol that performs a security-related function and applies cryptographic methods. ...


Cryptographic protocols have been developed for a wide range of problems, including relatively simple ones like interactive proofs,[22] secret sharing,[23][24] and zero-knowledge,[25] and much more complex ones like electronic cash[26] and secure multiparty computation.[27] For interactive proof, see interactive proof system or interactive theorem proving. ... Each secret share is a plane, and the secret is the point at which three shares intersect. ... In cryptography, a zero-knowledge proof is an interactive method for one party to prove to another that a (usually mathematical) statement is true, without revealing anything other than the veracity of the statement. ... Electronic money (or digital money) refers to cash and transactions using electronic means, encompassing the use of computer networks (such as the Internet) and digital stored value systems. ... In cryptography, secure multiparty computation is a problem that was initially suggested by Andrew C. Yao in a 1982 paper. ...


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. A software bug is an error, flaw, mistake, failure, or fault in a computer program that prevents it from behaving as intended (e. ... Mathematical logic is a subfield of mathematics that is concerned with formal systems in relation to the way that they encode intuitive concepts of mathematical objects such as sets and numbers, proofs, and computation. ... Burrows-Abadi-Needham logic (also known as the BAN logic) uses postulates and definitions -- like all axiomatic systems -- to analyze authentication protocols. ... In cryptography, concrete security or exact security is a practice-oriented approach that aims to give more precise estimates of the computational complexities of adversarial tasks than polynomial equivalence would allow. ...


The study of how best to implement and integrate cryptography in applications is itself a distinct field, see: cryptographic engineering and security engineering. This article is an overview of cryptographic engineering which notes at least some of the differences between ordinary engineering and the cryptographic sort. ... Security engineering is the field of engineering dealing with the security and integrity of real-world systems. ...


Legal issues involving cryptography

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. For the band, see The Police. ... Privacy has no definite boundaries and it has different meanings for different people. ...


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, like tanks and nuclear weapons.[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. Since World War II, Western governments, including the U.S. and its NATO allies have regulated the export of cryptography for national security considerations. ... Combatants Allied powers: China France Great Britain Soviet Union United States and others Axis powers: Germany Italy Japan and others Commanders Chiang Kai-shek Charles de Gaulle Winston Churchill Joseph Stalin Franklin Roosevelt Adolf Hitler Benito Mussolini Hideki Tōjō Casualties Military dead: 17,000,000 Civilian dead: 33,000... Munition is often defined as a synonyn for ammunition. ...


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 of 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.[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] Since World War II, Western governments, including the U.S. and its NATO allies have regulated the export of cryptography for national security considerations. ... Philip Zimmermann (born February 12, 1954) is the creator of Pretty Good Privacy (PGP), the most widely used email encryption software in the world. ... PGP Encryption (Pretty Good Privacy) is a computer program that provides cryptographic privacy and authentication. ... Source code (commonly just source or code) is any series of statements written in some human-readable computer programming language. ... RSA, The Security Division of EMC Corporation (NYSE: EMC), is headquartered in Bedford, Massachusetts, and maintains offices in Ireland, the United Kingdom, Singapore, and Japan. ... The Federal Bureau of Investigation (FBI) is the primary investigative arm of the United States Department of Justice (DOJ), serving as both a federal criminal investigative body and a domestic intelligence agency. ... Daniel Julius Bernstein (sometimes known simply as djb) is a professor at the University of Illinois at Chicago, a mathematician, a cryptologist, and a programmer. ... The University of California, Berkeley (also known as Cal, UC Berkeley, UCB, or simply Berkeley) is a prestigious, public, coeducational university situated in the foothills of Berkeley, California to the east of San Francisco Bay, overlooking the Golden Gate and its bridge. ... The First Amendment may refer to the: First Amendment to the United States Constitution – part of the Bill of Rights. ... Bernstein v. ... Freedom of speech is the concept of being able to speak freely without censorship. ...


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 browser's; 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. The Wassenaar Arrangement on Export Controls for Conventional Arms and Dual-Use Goods and Technologies is an arms control arrangement with 39 participating states. ... An example of a web browser (Internet Explorer), displaying the English Wikipedia main page. ... Mozilla Firefox is a graphical web browser developed by the Mozilla Corporation and a large community of external contributors. ... Internet Explorer, abbreviated IE or MSIE is a web browser from Microsoft currently sold as part of Microsoft Windows. ... This article or section does not adequately cite its references or sources. ... This article or section does not adequately cite its references or sources. ... Mozilla Thunderbird is a free, cross-platform e-mail and news client developed by the Mozilla Foundation. ... Microsoft Outlook or Outlook (full name Microsoft Office Outlook since Outlook 2003) is a personal information manager from Microsoft, and is part of the Microsoft Office suite. ... This article does not cite any references or sources. ... The Internet Message Access Protocol (commonly known as IMAP, and previously called Interactive Mail Access Protocol) is an application layer Internet protocol used for accessing email on a remote server from a local client. ... In computing, local e-mail clients use the Post Office Protocol version 3 (POP3), an application-layer Internet standard protocol, to retrieve e-mail from a remote server over a TCP/IP connection. ... S/MIME (Secure / Multipurpose Internet Mail Extensions) is a standard for public key encryption and signing of e-mail encapsulated in MIME. // S/MIME was originally developed by RSA Data Security Inc. ... There are two different meanings of the word cryptosystem. ...


NSA involvement

See also: Clipper chip

Another contentious issue connected to cryptography in the United States is the influence of the National Security Agency in 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.[37] DES was designed to be secure against 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. The Clipper chip is a chipset that was developed and promoted by the U.S. Government as an encryption device to be adopted by telecommunications companies for voice transmission. ... Lieutenant General Keith B. Alexander, 16th and current director of the NSA (2005–). The National Security Agency/Central Security Service (NSA/CSS) is the United States governments cryptologic organization that was officially established on November 4, 1952. ... The Data Encryption Standard (DES) is a cipher (a method for encrypting information) selected as an official Federal Information Processing Standard (FIPS) for the United States in 1976, and which has subsequently enjoyed widespread use internationally. ... As a non-regulatory agency of the United States Department of Commerce’s Technology Administration, the National Institute of Standards (NIST) develops and promotes measurement, standards, and technology to enhance productivity, facilitate trade, and improve the quality of life. ... Differential cryptanalysis is a general form of cryptanalysis applicable primarily to block ciphers, but also to stream ciphers and cryptographic hash functions. ... Steven Levy Steven Levy (born 1951) is an American journalist who has written several books on computers, technology, cryptography, the Internet, cybersecurity, and privacy. ...


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] The Clipper chip is a chipset that was developed and promoted by the U.S. Government as an encryption device to be adopted by telecommunications companies for voice transmission. ... Capstone is the name of a United States government long-term project to develop cryptography standards for public and government use. ... In cryptography, Skipjack is a block cipher — an algorithm for encryption — developed by the U.S. National Security Agency (NSA). ... In cryptography, Kerckhoffs principle (also called Kerckhoffs assumption, axiom or law) was stated by Auguste Kerckhoffs in the 19th century: a cryptosystem should be secure even if everything about the system, except the key, is public knowledge. ... Key escrow is an arrangement in which the keys needed to decrypt encrypted data are held in escrow by a third party, so that someone else (typically government agencies) can obtain them to decrypt messages which they suspect to be relevant to national security. ...


Digital Rights Management

Main Article: 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, 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.[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. Digital rights management (DRM) is an umbrella term referring to technologies used by publishers or copyright owners to control access to or usage of digital data or hardware, and to restrictions associated with a specific instance of a digital work or device. ... Copyright symbol Copyright is a set of exclusive rights regulating the use of a particular expression of an idea or information. ... Copyright symbol Copyright is a set of exclusive rights regulating the use of a particular expression of an idea or information. ... William Jefferson Bill Clinton (born William Jefferson Blythe III[1] on August 19, 1946) was the 42nd President of the United States, serving from 1993 to 2001. ... The Digital Millennium Copyright Act (DMCA) is a United States copyright law which implements two 1996 WIPO treaties. ... The Federal Bureau of Investigation (FBI) is the primary investigative arm of the United States Department of Justice (DOJ), serving as both a federal criminal investigative body and a domestic intelligence agency. ... The United States Department of Justice (DOJ) is a Cabinet department in the United States government designed to enforce the law and defend the interests of the United States according to the law and to ensure fair and impartial administration of justice for all Americans. ... Niels Ferguson is a Dutch cryptographic engineer and consultant. ... Intel Corporation (NASDAQ: INTC; SEHK: 4335) is the worlds largest semiconductor company and the inventor of the x86 series of microprocessors, the processors found in many personal computers. ... Alan Cox at FOSS.IN/2005 Alan Cox (born 1968) is a computer programmer heavily involved in the development of the Linux kernel since its early days (1991). ... The Linux kernel is a Unix-like operating system kernel. ... Edward William Felten (born March 25, 1963) is a professor of computer science and public affairs at Princeton University. ... Dmitry Sklyarov (Дмитрий Скляров) (born December 18, 1974) is a Russian computer programmer best known for his 2001 run-in with American law enforcement over software copyright restrictions. ... The Directive 2001/29/EC of the European Parliament and of the Council of 22 May 2001 on the harmonisation of certain aspects of copyright and related rights in the information society, commonly known as the EU Copyright Directive or short EUCD, is the European Unions implementation of the... DVD (Digital Versatile Disc or Digital Video Disc) is an optical disc storage media format that can be used for data storage, including movies with high video and sound quality. ... HD-DVD disc HD DVD (High Density Digital Versatile Disc) is a digital optical media format which is being developed as one standard for high-definition DVD. HD DVD is similar to the competing Blu-ray Disc, which also uses the same CD sized (120 mm diameter) optical data storage... The Motion Picture Association of America (MPAA) is a non-profit trade association formed to advance the interests of movie studios. ... The AACS encryption key controversy arose in April 2007 when the Motion Picture Association of America and the Advanced Access Content System Licensing Administrator, LLC (AACS LA) began issuing Digital Millennium Copyright Act (DMCA) violation notices [1] to websites publishing a 16-byte number, represented in hexadecimal as 09 F9... For fair use in trademark law, see Fair use (US trademark law). ... Freedom of speech is the right to freely say what one pleases, as well as the related right to hear what others have stated. ...


See also

Cryptography Portal
Look up Cryptography in
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Image File history File links Crypto_key. ... Wikipedia does not have an article with this exact name. ... Wiktionary (a portmanteau of wiki and dictionary) is a multilingual, Web-based project to create a free content dictionary, available in over 150 languages. ... Image File history File links Commons-logo. ... The Wikimedia Commons (also called Wikicommons) is a repository of free content images, sound and other multimedia files. ... Image File history File links Wikiversity-logo-Snorky. ... Wikiversity logo Wikiversity is a Wikimedia Foundation beta project[1], devoted to learning materials and activities, located at www. ... This article is intended to be an analytic glossary, or alternatively, an organized collection of annotated pointers. ... See also: Category:Cryptographers for an exhaustive list. ... Johannes Trithemius Polygraphiae (1518) — the first printed book on cryptology. ... This is a list of important publications in computer science, organized by field. ... This is a list of unsolved problems in computer science. ... The International Association for Cryptologic Research (IACR) is a non-profit scientific organization whose purpose is to further research in cryptology and related fields. ... The Chaos Computer Club (CCC) is one of the biggest and most influental hacker organisations. ...

Further reading

See Books on cryptography for a more detailed list. Johannes Trithemius Polygraphiae (1518) — the first printed book on cryptology. ...

The Codebreakers - The Story of Secret Writing (ISBN 0684831309) is a book written by David Kahn in 1967 chronicling the history of cryptology from ancient Egypt to the time of its writing. ... David Kahn is a US historian, journalist and writer. ... The Code Book: The Evolution of Secrecy from Mary, Queen of Scots to Quantum Cryptography is a book written by Simon Singh and published in 1999 by Doubleday of New York; ISBN 0-385-49531-5 The Code Book covers a diverse set of historical topics including The Man in... Simon Singh Simon Lehna Singh (born 1964) is an Indian-British author of Punjabi background with a doctorate in physics from Emmanuel College, Cambridge, who has specialized in writing about mathematical and scientific topics in an accessible manner. ... Crypto: How the Code Rebels Beat the Government Saving Privacy in the Digital Age (ISBN 0140244328) is a book written by Steven Levy about cryptography, and was published in 2001. ... Steven Levy Steven Levy (born 1951) is an American journalist who has written several books on computers, technology, cryptography, the Internet, cybersecurity, and privacy. ... The Clipper chip is a chipset that was developed and promoted by the U.S. Government as an encryption device to be adopted by telecommunications companies for voice transmission. ... Bernstein v. ... Bruce Schneier Bruce Schneier (born January 15, 1963) is an American cryptographer, computer security specialist, and writer. ... Bruce Schneier Bruce Schneier (born January 15, 1963) is an American cryptographer, computer security specialist, and writer. ... Phillip Rogaway is a professor of computer science at the University of California, Davis. ... Mihir Bellare is a cryptographer at the University of California, San Diego. ... Spy and Secret agent redirect here. ... Cryptology is an umbrella term for cryptography and cryptanalysis. ... (19th century - 20th century - 21st century - more centuries) Decades: 1900s 1910s 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s The 20th century lasted from 1901 to 2000 in the Gregorian calendar (often from (1900 to 1999 in common usage). ... James Gannon is a freelance writer and producer of documentaries for NBC News. ... Cryptonomicon is a 1999 novel by Neal Stephenson. ... Neal Town Stephenson (born October 31, 1959) is an American writer, known primarily for his science fiction works in the postcyberpunk genre with a penchant for explorations of society, mathematics, currency, and the history of science. ... The plugboard, keyboard, lamps and finger-wheels of the rotors emerging from the inner lid of a three-rotor German military Enigma machine (version with labels) The Enigma machine was a cipher machine used to encrypt and decrypt secret messages. ... Clifford B. Hicks was born in 1920 in Marshalltown, Iowa, a town similar to Riverton, Indiana (where the Alvin Fernald series is set). ... Sarah Flannery (born 1982, County Cork, Ireland) was, at sixteen years old, the winner of the 1999 Esat Young Scientist Exhibition for development of the Cayley-Purser algorithm, based on work she had done with researchers at Baltimore Technologies during a brief internship there. ... CrypTool is a free software illustrating the cryptographic concepts. ...

External links

References

  1. ^ Eerdmans Commentary on the Bible, James D G Dunn, John W Rogerson, eds., Wm. B. Eerdmans Publishing, 2003, ISBN 0-8028-3711-5
  2. ^ Kama Sutra, Sir Richard F. Burton, translator, Part I, Chapter III, 44th and 45th arts.
  3. ^ a b c David Kahn, The Codebreakers, 1967, ISBN 0-684-83130-9.
  4. ^ 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.
  5. ^ 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)
  6. ^ a b Oded Goldreich, Foundations of Cryptography, Volume 1: Basic Tools, Cambridge University Press, 2001, ISBN 0-521-79172-3
  7. ^ a b c d e f AJ Menezes, PC van Oorschot, and SA Vanstone, Handbook of Applied Cryptography ISBN 0-8493-8523-7.
  8. ^ FIPS PUB 197: The official Advanced Encryption Standard.
  9. ^ NCUA letter to credit unions, July 2004
  10. ^ RFC 2440 - Open PGP Message Format
  11. ^ SSH at windowsecurity.com by Pawel Golen, July 2004
  12. ^ a b Bruce Schneier, Applied Cryptography, 2nd edition, Wiley, 1996, ISBN 0-471-11709-9.
  13. ^ Whitfield Diffie and Martin Hellman, "Multi-user cryptographic techniques" [Diffie and Hellman, AFIPS Proceedings 45, pp109–112, June 8, 1976].
  14. ^ 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.
  15. ^ David Kahn, "Cryptology Goes Public", 58 Foreign Affairs 141, 151 (fall 1979), p. 153.
  16. ^ 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
  17. ^ Clifford Cocks. A Note on 'Non-Secret Encryption', CESG Research Report, 20 November 1973.
  18. ^ "Shannon": Claude Shannon and Warren Weaver, "The Mathematical Theory of Communication", University of Illinois Press, 1963, ISBN 0-252-72548-4
  19. ^ Pascal Junod, "On the Complexity of Matsui's Attack", SAC 2001.
  20. ^ Dawn Song, David Wagner, and Xuqing Tian, "Timing Analysis of Keystrokes and Timing Attacks on SSH", In Tenth USENIX Security Symposium, 2001.
  21. ^ 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.
  22. ^ László Babai. "Trading group theory for randomness". Proceedings of the Seventeenth Annual Symposium on the Theory of Computing, ACM, 1985.
  23. ^ G. Blakley. "Safeguarding cryptographic keys." In Proceedings of AFIPS 1979, volume 48, pp. 313–317, June 1979.
  24. ^ A. Shamir. "How to share a secret." In Communications of the ACM, volume 22, pp. 612–613, ACM, 1979.
  25. ^ 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.
  26. ^ S. Brands, "Untraceable Off-line Cash in Wallets with Observers", In Advances in Cryptology — Proceedings of CRYPTO, Springer-Verlag, 1994.
  27. ^ 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.
  28. ^ 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.
  29. ^ 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.
  30. ^ D. Song, "Athena, an automatic checker for security protocol analysis", In Proceedings of the 12th IEEE Computer Security Foundations Workshop (CSFW), IEEE, 1999.
  31. ^ a b RSA Laboratories' Frequently Asked Questions About Today's Cryptography
  32. ^ Cryptography & Speech from Cyberlaw
  33. ^ "Case Closed on Zimmermann PGP Investigation", press note from the IEEE.
  34. ^ 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. 
  35. ^ Bernstein v USDOJ, 9th Circuit court of appeals decision.
  36. ^ The Wassenaar Arrangement on Export Controls for Conventional Arms and Dual-Use Goods and Technologies
  37. ^ "The Data Encryption Standard (DES)" from Bruce Schneier's CryptoGram newsletter, June 15, 2000
  38. ^ Coppersmith, D. (May 1994). "The Data Encryption Standard (DES) and its strength against attacks" (PDF). IBM Journal of Research and Development 38 (3): 243. 
  39. ^ E. Biham and A. Shamir, "Differential cryptanalysis of DES-like cryptosystems", Journal of Cryptology, vol. 4 num. 1, pp. 3–72, Springer-Verlag, 1991.
  40. ^ Levy, pg. 56
  41. ^ Digital Millennium Copyright Act
Cryptography
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  Results from FactBites:
 
Cryptography - Wikipedia, the free encyclopedia (4089 words)
Cryptography or cryptology is a field of mathematics and computer science concerned with information security and related issues, particularly encryption and authentication.
Cryptography is also considered a branch of engineering, but it is considered to be an unusual one as it deals with active, intelligent and malevolent opposition (see cryptographic engineering and security engineering).
Cryptography exports from the US (and in much of the rest of the developed world) are less strictly regulated now than in the past, though encryption is still defined as a munition.
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