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Encyclopedia > Cryptanalysis
Close-up of the rotors in a Fialka cipher machine
Close-up of the rotors in a Fialka cipher machine

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. Typically, this involves finding a secret key. In non-technical language, this is the practice of codebreaking or cracking the code, although these phrases also have a specialised technical meaning (see code). Closeup of the rotor stack inside a FIALKA cipher machine. ... Closeup of the rotor stack inside a FIALKA cipher machine. ... The advanced Russian cipher machine Fialka (M-125) has only recently been made known to the public. ... This article is about algorithms for encryption and decryption. ... Secrecy is the condition of hiding information from others. ... A key is a piece of information that controls the operation of a cryptography algorithm. ... 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. ...


"Cryptanalysis" is also used to refer to any attempt to circumvent the security of other types of cryptographic algorithms and protocols in general, and not just encryption. However, cryptanalysis usually excludes methods of attack that do not primarily target weaknesses in the actual cryptography, such as bribery, physical coercion, burglary, keystroke logging, and social engineering, although these types of attack are an important concern and are often more effective than traditional cryptanalysis. Cryptography (from Greek kryptós, hidden, and gráphein, to write) is, traditionally, the study of means of converting information from its normal, comprehensible form into an incomprehensible format, rendering it unreadable without secret knowledge — the art of encryption. ... Flowcharts are often used to graphically represent algorithms. ... A cryptographic protocol is an abstract or concrete protocol that performs a security-related function and applies cryptographic methods. ... Encrypt redirects here. ... 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. ... 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. ... In cryptography, rubber-hose cryptanalysis is the extraction of cryptographic secrets from a person by torture, in contrast to a mathematical or technical cryptanalytic attack. ... Keystroke logging (often called keylogging) is a diagnostic tool used in software development that captures the users keystrokes. ... 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. ...


Even though the goal has been the same, the methods and techniques of cryptanalysis have changed drastically through the history of cryptography, adapting to increasing cryptographic complexity, ranging from the pen-and-paper methods of the past, through machines like Enigma in World War II, to the computer-based schemes of the present. The results of cryptanalysis have also changed — it is no longer possible to have unlimited success in codebreaking, and there is a hierarchical classification of what constitutes a rare practical attack. In the mid-1970s, a new class of cryptography was introduced: asymmetric cryptography. Methods for breaking these cryptosystems are typically radically different from before, and usually involve solving carefully-constructed problems in pure mathematics, the best-known being integer factorization. For a discussion of how Enigma-derived intelligence was put to use, see Ultra (WWII intelligence). ... 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... In cryptography, an asymmetric key algorithm uses a pair of different, though related, cryptographic keys to encrypt and decrypt. ... There are two different meanings of the word cryptosystem. ... Broadly speaking, pure mathematics is mathematics motivated entirely for reasons other than application. ... Prime decomposition redirects here. ...

Contents

History of cryptanalysis

Main article: History of cryptography

Cryptanalysis has coevolved together with cryptography, and the contest can be traced through the history of cryptography—new ciphers being designed to replace old broken designs, and new cryptanalytic techniques invented to crack the improved schemes . In practice, they are viewed as two sides of the same coin: in order to create secure cryptography, you have to design against possible cryptanalysis. The history of cryptography begins thousands of years ago. ... Bumblebees and the flowers they pollinate co-evolve so that the flower is dependent on the bee and the bee is dependent on the flower for survival In Biology, Co-evolution is the mutual evolutionary influence between two species that become dependent on each other. ... The history of cryptography begins thousands of years ago. ... This article is about algorithms for encryption and decryption. ...


Classical cryptanalysis

First page of Al-Kindi's 9th century Manuscript on Deciphering Cryptographic Messages
First page of Al-Kindi's 9th century Manuscript on Deciphering Cryptographic Messages

Although the actual word "cryptanalysis" is relatively recent (it was coined by William Friedman in 1920), methods for breaking codes and ciphers are much older. The first known recorded explanation of cryptanalysis was given by 9th century Arabian polymath Abu Yusuf Yaqub ibn Ishaq al-Sabbah Al-Kindi in A Manuscript on Deciphering Cryptographic Messages. This treatise includes a description of the method of frequency analysis (Ibrahim Al-Kadi, 1992- ref-3). The first page of al-Kindis manuscript On Deciphering Cryptographic Messages, containing the oldest known description of cryptanalysis by frequency analysis. ... The first page of al-Kindis manuscript On Deciphering Cryptographic Messages, containing the oldest known description of cryptanalysis by frequency analysis. ... For the Christian theologian, see Abd al-Masih ibn Ishaq al-Kindi. ... William Frederick Friedman (September 24, 1891 - November 12, 1969) served as a US Army cryptologist, running the research division of the Armys Signals Intelligence Service (SIS) through the 1930s and its follow-on services right into the 1950s. ... 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. ... This article is about algorithms for encryption and decryption. ... As a means of recording the passage of time the 9th century was the century that lasted from 801 to 900. ... For other uses, see Arab (disambiguation). ... Leonardo da Vinci, a polymath, is seen as the epitome of the related term, Renaissance Man A polymath (Greek polymathÄ“s, πολυμαθής, having learned much)[1][2] is a person with encyclopedic, broad, or varied knowledge or learning. ... Al-Kindi (Arabic: أبو يعقوب يوسف بن إسحاق الكندي) was a Arabn philosopher, scientist and ophthalmologist. ... 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. ... Ibrahim A. Al-Kadi, Ph. ...


Frequency analysis is the basic tool for breaking most classical ciphers. In natural languages, certain letters of the alphabet appear more frequently than others; in English, "E" is likely to be the most common letter in any sample of plaintext. Similarly, the digraph "TH" is the most likely pair of letters in English, and so on. Frequency analysis relies on a cipher failing to hide these statistics. For example, in a simple substitution cipher (where each letter is simply replaced with another), the most frequent letter in the ciphertext would be a likely candidate for "E". 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. ... In cryptography, a classical cipher is a type of cipher used historically but which now have fallen, for the most part, into disuse. ... ABCs redirects here. ... The English language is a West Germanic language that originates in England. ... For other uses, see E (disambiguation). ... This article is about cryptography. ... Note: This page or section contains IPA phonetic symbols in Unicode. ... This article is about the field of statistics. ... 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. ...


In practice, frequency analysis relies as much on linguistic knowledge as it does on statistics, but as ciphers became more complex, mathematics became more important in cryptanalysis. This change was particularly evident during World War II, where efforts to crack Axis ciphers required new levels of mathematical sophistication. Moreover, automation was first applied to cryptanalysis in that era with the Polish Bomba device, use of punched card equipment, and in the Colossus — one of the earliest computers (arguably the first programmable electronic digital computer). For the journal, see Linguistics (journal). ... This article is about the field of statistics. ... For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... 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... Black: Zenith of the Axis Powers Capital Not applicable Political structure Military alliance Historical era World War II  - Tripartite Pact September 27, 1940  - Anti-Comintern Pact November 25, 1936  - Pact of Steel May 22, 1939  - Dissolved 1945 This article is about the independent countries (states) that comprised the Axis powers. ... Cryptologic bomb. ... A CTR census machine, utilizing a punched card system. ... A Colossus Mark II computer. ...


Modern cryptanalysis

Replica of a Bombe device
Replica of a Bombe device

Even though computation was used to great effect in cryptanalysis in World War II, it also made possible new methods of cryptography orders of magnitude more complex than ever before. Taken as a whole, modern cryptography has become much more impervious to cryptanalysis than the pen-and-paper systems of the past, and now seems to have the upper hand against pure cryptanalysis. The historian David Kahn notes, "Many are the cryptosystems offered by the hundreds of commercial vendors today that cannot be broken by any known methods of cryptanalysis. Indeed, in such systems even a chosen plaintext attack, in which a selected plaintext is matched against its ciphertext, cannot yield the key that unlock other messages. In a sense, then, cryptanalysis is dead. But that is not the end of the story. Cryptanalysis may be dead, but there is - to mix my metaphors - more than one way to skin a cat.". [1] Kahn goes on to mention increased opportunities for interception, bugging, side channel attacks and quantum computers as replacements for the traditional means of cryptanalysis. Cardboard replica of a British Bombe made for the movie Enigma and now on display at Bletchley Park. ... Cardboard replica of a British Bombe made for the movie Enigma and now on display at Bletchley Park. ... The Bombe replicated the action of several Enigma machines wired together. ... An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. ... David Kahn is a US historian, journalist and writer. ... A bug is the common name for a covert listening device, usually a combination of a miniature radio transmitter with a microphone. ... In cryptography, a side channel attack is any attack based on information gained from the physical implementation of a cryptosystem, rather than theoretical weaknesses in the algorithms (compare cryptanalysis). ... Quantum cryptography, or quantum key distribution (QKD), uses quantum mechanics to guarantee secure communication. ...


Kahn may have been premature in his cryptanalysis postmortem; weak ciphers are not yet extinct, and cryptanalytic methods employed by intelligence agencies remain unpublished. In academia, new designs are regularly presented, and are also frequently broken: the 1984 block cipher Madryga was found to be susceptible to ciphertext-only attacks in 1998; FEAL-4, proposed as a replacement for the DES standard encryption algorithm, was demolished by a spate of attacks from the academic community, many of which are entirely practical. In industry, too, ciphers are not free from flaws: for example, the A5/1, A5/2 and CMEA algorithms, used in mobile phone technology, can all be broken in hours, minutes or even in real-time using widely-available computing equipment. In 2001, Wired Equivalent Privacy (WEP), a protocol used to secure Wi-Fi wireless networks, was shown to be susceptible to a practical related-key attack. Academia is a collective term for the scientific and cultural community engaged in higher education and research, taken as a whole. ... Encryption Decryption In cryptography, a block cipher is a symmetric key cipher which operates on fixed-length groups of bits, termed blocks, with an unvarying transformation. ... In cryptography, Madryga is a block cipher created in 1984 by W. E. Madryga. ... 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. ... General Designer(s) Akihiro Shimizu and Shoji Miyaguchi (NTT) First published FEAL-4 in 1987; FEAL-N/NX in 1990 Derived from - Cipher(s) based on this design - Algorithm detail Block size(s) 64 bits Key size(s) 64 bits (128 bits for FEAL-NX) Structure Feistel network Number of... 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. ... A5/1 is a stream cipher used to provide over-the-air communication privacy in the GSM cellular telephone standard. ... A5/2 is a stream cipher used to provide voice privacy in the GSM cellular telephone protocol. ... In cryptography, the Cellular Message Encryption Algorithm (CMEA) is a block cipher which was used for securing mobile phones in the United States. ... Wired Equivalent Privacy (WEP), sometimes inaccurately referred to as Wireless Encryption Protocol, is a scheme to secure IEEE 802. ... Wi-Fi (IPA: ) is the common name for a popular wireless technology used in home networks, mobile phones, video games and more. ... While the term wireless network may technically be used to refer to any type of computer network that is wireless, the term is most commonly used to refer to a telecommunications network whose interconnections between nodes is implemented without the use of wires, such as a computer network (which is... In cryptography, a related-key attack is any form of cryptanalysis where the attacker can observe the operation of a cipher under several different keys whose values are initially unknown, but where some mathematical relationship connecting the keys is known to the attacker. ...


The results of cryptanalysis

The decrypted Zimmermann Telegram.
The decrypted Zimmermann Telegram.

Successful cryptanalysis has undoubtedly influenced history; the ability to read the presumed-secret thoughts and plans of others can be a decisive advantage, and never more so than during wartime. For example, in World War I, the breaking of the Zimmermann Telegram was instrumental in bringing the United States into the war. In World War II, the cryptanalysis of the German ciphers — including the Enigma machine and the Lorenz cipher — has been credited with everything between shortening the end of the European war by a few months to determining the eventual result (see ULTRA). The United States also benefited from the cryptanalysis of the Japanese PURPLE code (see MAGIC). Zimmermann Telegram decrypted and translated This image is in the public domain in the United States and possibly other jurisdictions. ... Zimmermann Telegram decrypted and translated This image is in the public domain in the United States and possibly other jurisdictions. ... The Zimmermann Telegram (or Zimmermann Note; German: Zimmermann-Depesche; Spanish: Telegrama Zimmermann) was a coded telegram dispatched by the Foreign Secretary of the German Empire, Arthur Zimmermann, on January 16, 1917, to the German ambassador in the United States of America, Johann von Bernstorff, at the height of World War... “The Great War ” redirects here. ... The Zimmermann Telegram (or Zimmermann Note; German: Zimmermann-Depesche; Spanish: Telegrama Zimmermann) was a coded telegram dispatched by the Foreign Secretary of the German Empire, Arthur Zimmermann, on January 16, 1917, to the German ambassador in the United States of America, Johann von Bernstorff, at the height of World War... 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... For a discussion of how Enigma-derived intelligence was put to use, see Ultra (WWII intelligence). ... For the fish, see Tuna. ... Ultra (sometimes capitalized ULTRA) was the name used by the British for intelligence resulting from decryption of German communications in World War II. The term eventually became the standard designation in both Britain and the United States for all intelligence from high-level cryptanalytic sources. ... This article is about the color. ... In World War II, Magic was the United States codename for intelligence derived from the cryptanalysis of PURPLE, a Japanese foreign office cipher. ...


Governments have long recognised the potential benefits of cryptanalysis for intelligence, both military and diplomatic, and established dedicated organisations devoted to breaking the codes and ciphers of other nations, for example, GCHQ and the NSA, organisations which are still very active today. In 2004, it was reported that the United States had broken Iranian ciphers. (It is unknown, however, whether this was pure cryptanalysis, or whether other factors were involved: [1]). Military intelligence (abbreviated MI, int [Commonwealth], or intel [U.S.]), is a military discipline that focuses on information gathering, analysis, and dissemination about enemy units, terrain, and the weather in an area of operations. ... 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). ... NSA can stand for: National Security Agency of the USA The British Librarys National Sound Archive This page concerning a three-letter acronym or abbreviation is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ...


Characterising attacks

Cryptanalytic attacks vary in potency and how much of a threat they pose to real-world cryptosystems. A certificational weakness is a theoretical attack that is unlikely to be applicable in any real-world situation; the majority of results found in modern cryptanalytic research are of this type. Essentially, the practical importance of an attack is dependent on the answers to the following three questions: There are two different meanings of the word cryptosystem. ...

  1. What knowledge and capabilities are needed as a prerequisite?
  2. How much additional secret information is deduced?
  3. How much effort is required? (What is the computational complexity?)

For other uses, see Knowledge (disambiguation). ... Complexity theory is part of the theory of computation dealing with the resources required during computation to solve a given problem. ...

Prior knowledge: scenarios for cryptanalysis

Cryptanalysis can be performed under a number of assumptions about how much can be observed or found out about the system under attack. As a basic starting point it is normally assumed that, for the purposes of analysis, the general algorithm is known; this is Kerckhoffs' principle of "the enemy knows the system". This is a reasonable assumption in practice — throughout history, there are countless examples of secret algorithms falling into wider knowledge, variously through espionage, betrayal and reverse engineering. (On occasion, ciphers have been reconstructed through pure deduction; for example, the German Lorenz cipher and the Japanese Purple code, and a variety of classical schemes). Flowcharts are often used to graphically represent algorithms. ... 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. ... Spy and Secret agent redirect here. ... Betrayal, as a form of deception or dismissal of prior presumptions, is the breaking or violation of a presumptive social contract (trust, or confidence) that produces moral and psychological conflict within a relationship amongst individuals, between organizations or between individuals and organizations. ... Reverse engineering (RE) is the process of taking something (a device, an electrical component, a software program, etc. ... For the fish, see Tuna. ... A fragment of an actual Purple machine found in Berlin at the end of WWII In the history of cryptography, 97-shiki-obun In-ji-ki (九七式欧文印字機) (System 97 Printing Machine for European Characters) or Angooki Taipu B (暗号機B型) (Type B Cipher Machine), codenamed PURPLE by the United States, was...


Other assumptions include:

These types of attack clearly differ in how plausible they would be to mount in practice. Although some are more likely than others, cryptographers will often take a conservative approach to security and assume the worst-case when designing algorithms, reasoning that if a scheme is secure even against unrealistic threats, then it should also resist real-world cryptanalysis as well. 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. ... This article is about algorithms for encryption and decryption. ... 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. ... 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. ... This article is about cryptography. ... 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. ... A chosen ciphertext attack is an attack on a cryptosystem in which the cryptanalyst chooses ciphertext and causes it to be decrypted with an unknown 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. ... An adaptive chosen ciphertext attack is an interactive form of chosen ciphertext attack in which an attacker sends a number of ciphertexts to be decrypted, then uses the results of these decryptions to select subsequent ciphertexts. ... In cryptography, a related-key attack is any form of cryptanalysis where the attacker can observe the operation of a cipher under several different keys whose values are initially unknown, but where some mathematical relationship connecting the keys is known to the attacker. ...


The assumptions are often more realistic than they might seem upon first glance. For a known-plaintext attack, the cryptanalyst might well know or be able to guess at a likely part of the plaintext, such as an encrypted letter beginning with "Dear Sir", or a computer session starting with "LOGIN:". A chosen-plaintext attack is less likely, but it is sometimes plausible: for example, you could convince someone to forward a message you have given them, but in encrypted form. Related-key attacks are mostly theoretical, although they can be realistic in certain situations, for example, when constructing cryptographic hash functions using a block cipher. This article is about algorithms for encryption and decryption. ... 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. ... Encryption Decryption In cryptography, a block cipher is a symmetric key cipher which operates on fixed-length groups of bits, termed blocks, with an unvarying transformation. ...


Classifying success in cryptanalysis

The results of cryptanalysis can also vary in usefulness. For example, cryptographer Lars Knudsen (1998) classified various types of attack on block ciphers according to the amount and quality of secret information that was discovered: Lars R. Knudsen Lars Ramkilde Knudsen (born February 21, 1962) is a Danish researcher in cryptography, particularly interested in the design and analysis of block ciphers, hash functions and message authentication codes (MACs). ... Encryption Decryption In cryptography, a block cipher is a symmetric key cipher which operates on fixed-length groups of bits, termed blocks, with an unvarying transformation. ...

  • Total break — the attacker deduces the secret key.
  • Global deduction — the attacker discovers a functionally equivalent algorithm for encryption and decryption, but without learning the key.
  • Instance (local) deduction — the attacker discovers additional plaintexts (or ciphertexts) not previously known.
  • Information deduction — the attacker gains some Shannon information about plaintexts (or ciphertexts) not previously known.
  • Distinguishing algorithm — the attacker can distinguish the cipher from a random permutation.

Similar considerations apply to attacks on other types of cryptographic algorithm. A key is a piece of information that controls the operation of a cryptography algorithm. ... Flowcharts are often used to graphically represent algorithms. ... Claude Shannon In information theory, the Shannon entropy or information entropy is a measure of the uncertainty associated with a random variable. ... Permutation is the rearrangement of objects or symbols into distinguishable sequences. ...


Complexity

Attacks can also be characterised by the amount of resources they require. This can be in the form of:

  • Time — the number of "primitive operations" which must be performed. This is quite loose; primitive operations could be basic computer instructions, such as addition, XOR, shift, and so forth, or entire encryption methods.
  • Memory — the amount of storage required to perform the attack.
  • Data — the quantity of plaintexts and ciphertexts required.

In academic cryptography, a weakness or a break in a scheme is usually defined quite conservatively. Bruce Schneier sums up this approach: "Breaking a cipher simply means finding a weakness in the cipher that can be exploited with a complexity less than brute force. Never mind that brute-force might require 2128 encryptions; an attack requiring 2110 encryptions would be considered a break...simply put, a break can just be a certificational weakness: evidence that the cipher does not perform as advertised." (Schneier, 2000). Exclusive disjunction (usual symbol xor) is a logical operator that results in true if one of the operands (not both) is true. ...


Cryptanalysis of asymmetric cryptography

Asymmetric cryptography (or public key cryptography) is cryptography that relies on using two keys; one private, and one public. Such ciphers invariably rely on "hard" mathematical problems as the basis of their security, so an obvious point of attack is to develop methods for solving the problem. The security of two-key cryptography depends on mathematical questions in a way that single-key cryptography generally does not, and conversely links cryptanalysis to wider mathematical research in a new way. In cryptography, an asymmetric key algorithm uses a pair of different, though related, cryptographic keys to encrypt and decrypt. ... Public key cryptography is a form of cryptography which generally allows users to communicate securely without having prior access to a shared secret key, by using a pair of cryptographic keys, designated as public key and private key, which are related mathematically. ... A mathematical problem is a problem that can be solved with the help of mathematics. ...


Asymmetric schemes are designed around the (conjectured) difficulty of solving various mathematical problems. If an improved algorithm can be found to solve the problem, then the system is weakened. For example, the security of the Diffie-Hellman key exchange scheme depends on the difficulty of calculating the discrete logarithm. In 1983, Don Coppersmith found a faster way to find discrete logarithms (in certain groups), and thereby requiring cryptographers to use larger groups (or different types of groups). RSA's security depends (in part) upon the difficulty of integer factorization — a breakthrough in factoring would impact the security of RSA. In mathematics, a conjecture is a mathematical statement which appears likely to be true, but has not been formally proven to be true under the rules of mathematical logic. ... Diffie-Hellman (D-H) key exchange is a cryptographic protocol that allows two parties that have no prior knowledge of each other to jointly establish a shared secret key over an insecure communications channel. ... In mathematics, specifically in abstract algebra and its applications, discrete logarithms are group-theoretic analogues of ordinary logarithms. ... Don Coppersmith is a cryptographer and mathematician. ... Prime decomposition redirects here. ...


In 1980, one could factor a difficult 50-digit number at an expense of 1012 elementary computer operations. By 1984 the state of the art in factoring algorithms had advanced to a point where a 75-digit number could be factored in 1012 operations. Advances in computing technology also meant that the operations could be performed much faster, too. Moore's law predicts that computer speeds will continue to increase. Factoring techniques may continue do so as well, but will most likely depend on mathematical insight and creativity, neither of which has ever been successfully predictable. 150-digit numbers of the kind once used in RSA have been factored. The effort was greater than above, but was not unreasonable on fast modern computers. By the start of the 21st century, 150-digit numbers were no longer considered a large enough key size for RSA. Numbers with several hundred digits are still considered too hard to factor in 2005, though methods will probably continue to improve over time, requiring key size to keep pace or new algorithms to be used. Gordon Moores original graph from 1965 Growth of transistor counts for Intel processors (dots) and Moores Law (upper line=18 months; lower line=24 months) For the observation regarding information retrieval, see Mooers Law. ... In cryptography, the key size (alternatively key length) is the size of the digits used to create an encrypted text; it is therefore also a measure of the number of possible keys which can be used in a cipher, and the number of keys which must be tested to break... In cryptography, the key size (alternatively key length) is the size of the digits used to create an encrypted text; it is therefore also a measure of the number of possible keys which can be used in a cipher, and the number of keys which must be tested to break...


Another distinguishing feature of asymmetric schemes is that, unlike attacks on symmetric cryptosystems, any cryptanalysis has the opportunity to make use of knowledge gained from the public key. PKC, see PKC (disambiguation) Public-key cryptography is a form of modern cryptography which allows users to communicate securely without previously agreeing on a shared secret key. ...


Quantum computing applications for cryptanalysis

Quantum computers, which are still in the early phases of development, have potential use in cryptanalysis. For example, Shor's Algorithm could factor large numbers in polynomial time, in effect breaking some commonly used forms of public-key encryption. The Bloch sphere is a representation of a qubit, the fundamental building block of quantum computers. ... Shors algorithm is a quantum algorithm for factoring an integer N in O((log N)3) time and O(log N) space, named after Peter Shor. ... In computational complexity theory, polynomial time refers to the computation time of a problem where the time, m(n), is no greater than a polynomial function of the problem size, n. ...


By using Grover's algorithm on a quantum computer, brute-force key search can be made quadratically faster. However, this could be countered by increasing the key length. Grovers algorithm is a quantum algorithm for searching an unsorted database with N entries in O(N1/2) time and using O(logN) storage space (see big O notation). ...


Methods of cryptanalysis

Classical cryptanalysis:

Symmetric algorithms: 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. ... In cryptanalysis, the Kasiski examination or Kasiski test is a method of attacking polyalphabetic substitution ciphers, such as Vigenere ciphers. ... In cryptography, coincidence counting is the technique (invented by William F. Friedman) of putting two texts side-by-side and counting the number of times that a letter appears next to itself in both copies. ...

Hash functions: In cryptography, the boomerang attack is a method for the cryptanalysis of block ciphers, based on differential cryptanalysis invented by David Wagner in 1999. ... 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 cryptography, Davies attack [sic] is a dedicated statistical cryptanalysis method for attacking the Data Encryption Standard (DES). ... Differential cryptanalysis is a general form of cryptanalysis applicable primarily to block ciphers, but also to stream ciphers and cryptographic hash functions. ... This page meets Wikipedias criteria for speedy deletion. ... In cryptography, integral cryptanalysis is a cryptanalytic attack that is particularly applicable to block ciphers based around Substitution-permutation networks. ... In cryptography, linear cryptanalysis is a general form of cryptanalysis based on finding affine approximations to the action of a cipher. ... The Meet-in-the-middle attack is a cryptographic attack which, like the Birthday attack, makes use of a space-time tradeoff. ... In cryptography, mod n cryptanalysis is an attack applicable to block and stream ciphers. ... In cryptography, a related-key attack is any form of cryptanalysis where the attacker can observe the operation of a cipher under several different keys whose values are initially unknown, but where some mathematical relationship connecting the keys is known to the attacker. ... The idea of the slide attack was originally published by Edna Grossman and Bryant Tuckerman in an IBM Technical Report in 1977. ... New Scientist magazine featured the XSL attack in June 2003 with an article billed as Cipher crisis: the end of internet privacy. In cryptography, the XSL attack is a method of cryptanalysis for block ciphers. ...

Attack models: A birthday attack is a type of cryptographic attack which exploits the mathematics behind the birthday paradox, making use of a space-time tradeoff. ... Attack models specify how much information a cryptanalyst has access to when cracking an encrypted message. ...

Side channel attacks: 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. ... 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. ... In cryptography, a side channel attack is any attack based on information gained from the physical implementation of a cryptosystem, rather than theoretical weaknesses in the algorithms (compare cryptanalysis). ...

Network attacks: In cryptography, power analysis is a form of side channel attack in which the attacker studies the power consumption of a cryptographic hardware device (such as a smart card, tamperproof black box, microchip, etc). ... 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. ...

External attacks: It has been suggested that Mafia Fraud Attack be merged into this article or section. ... A replay attack is a form of network attack in which a valid data transmission is maliciously or fraudulently repeated or delayed. ...

It has been suggested that this article or section be merged into Black Bag Operation. ... In cryptography, rubber-hose cryptanalysis is the extraction of cryptographic secrets from a person by torture, in contrast to a mathematical or technical cryptanalytic attack. ...

See also

General

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. ... Decipherment is the analysis of documents written in ancient languages, where the language is unknown, or knowledge of the language has been lost. ... This article is intended to be an analytic glossary, or alternatively, an organized collection of annotated pointers. ...

National

The National Cipher Challenge is an annual cryptographic competition organised by the University of Southampton School of Mathematics. ... The Zendian Problem was a series of problems in traffic analysis and cryptanalysis devised by Lambros D. Callimahos as part of a course taught to National Security Agency cryptanalysts, whose graduates became members of the Dundee Society. ...

External links

Look up cryptanalysis in Wiktionary, the free dictionary.

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 151 languages. ...

References

  1. ^ David Kahn, Remarks on the 50th Anniversary of the National Security Agency, 2002 November 1.
David Kahn is a US historian, journalist and writer. ... Dr. Abraham Sinkov (1907-1998) was a US cryptanalyst. ... Ibrahim A. Al-Kadi, Ph. ... Cryptologia is a journal in cryptography published quarterly since 1977. ... David Kahn is a US historian, journalist and writer. ... 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. ... Lars R. Knudsen Lars Ramkilde Knudsen (born February 21, 1962) is a Danish researcher in cryptography, particularly the design and analysis of block ciphers, hash functions and message authentication codes (MACs). ... Bruce Schneier Bruce Schneier (born January 15, 1963) is an American cryptographer, computer security specialist, and writer. ... William Friedman. ... Military Cryptanalysis is a book by William F. Friedman written as a cryptanalysis text for NSA cryptanalysts. ... William Friedman. ... Military Cryptanalysis is a book by William F. Friedman written as a cryptanalysis text for NSA cryptanalysts. ... William Friedman. ... Military Cryptanalysis is a book by William F. Friedman written as a cryptanalysis text for NSA cryptanalysts. ... William Friedman. ... Military Cryptanalysis is a book by William F. Friedman written as a cryptanalysis text for NSA cryptanalysts. ... William Friedman. ... Lambros Demetrios Callimahos (December 16, 1910 – October 28, 1977) was a US Army cryptologist. ... Military Cryptanalytics (or MILCRYP as it is sometimes known) is a revision by Lambros D. Callimahos of the series of books written by William F. Friedman under the title Military Cryptanalysis. ... William Friedman. ... Lambros Demetrios Callimahos (December 16, 1910 – October 28, 1977) was a US Army cryptologist. ... Military Cryptanalytics (or MILCRYP as it is sometimes known) is a revision by Lambros D. Callimahos of the series of books written by William F. Friedman under the title Military Cryptanalysis. ... William Friedman. ... Lambros Demetrios Callimahos (December 16, 1910 – October 28, 1977) was a US Army cryptologist. ... Military Cryptanalytics (or MILCRYP as it is sometimes known) is a revision by Lambros D. Callimahos of the series of books written by William F. Friedman under the title Military Cryptanalysis. ... William Friedman. ... Lambros Demetrios Callimahos (December 16, 1910 – October 28, 1977) was a US Army cryptologist. ... Military Cryptanalytics (or MILCRYP as it is sometimes known) is a revision by Lambros D. Callimahos of the series of books written by William F. Friedman under the title Military Cryptanalysis. ... 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. ... The history of cryptography begins thousands of years ago. ... This article is intended to be an analytic glossary, or alternatively, an organized collection of annotated pointers. ... This article does not cite any references or sources. ... Encryption Decryption In cryptography, a block cipher is a symmetric key cipher which operates on fixed-length groups of bits, termed blocks, with an unvarying transformation. ... The operation of the keystream generator in A5/1, a LFSR-based stream cipher used to encrypt mobile phone conversations. ... A big random number is used to make a public-key/private-key pair. ... 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 cryptographic message authentication code (MAC) is a short piece of information used to authenticate a message. ... 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. ... This article is about hidden messages. ...

  Results from FactBites:
 
Linear Cryptanalysis: A Literature Survey (2070 words)
Perhaps the best introduction to Linear Cryptanalysis is the original article by Matsui, although continued development can be expected to have changed this original approach somewhat.
The complexity of differential cryptanalysis depends on the size of the largest entry in the XOR table, the total number of zeros in the XOR table, and the number of nonzero entries in the first column of that table [1], [3].
The complexity of differential cryptanalysis depends on the size of the largest entry in the XOR table, the total number of zeros in the XOR table, and the number of nonzero entries in the first column in that table [1], [8].
Careers in Cryptanalysis and Signals Analysis at National Security Agency (NSA) (363 words)
Cryptanalysis and Signals Analysis are core technical disciplines necessary for NSA to accomplish its mission and provide critical intelligence to the Nation's leaders.
Cryptanalysis is the analytic investigation of an information system with the goal of illuminating hidden aspects of that system.
Cryptanalysis is one of the core technical disciplines necessary for the National Security Agency (NSA) to accomplish its mission and provide critical intelligence to the Nation's leaders, and the need for Cryptanalysts will remain constant in our ever-changing global environment.
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