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Cryptanalysis (from the
Greek Greek may refer to: Greece Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group. *Greek language, a branch of the Indo-European language family. **Proto-Greek language, the assumed last common ancestor ...
''kryptós'', "hidden", and ''analýein'', "to analyze") refers to the process of analyzing
information system An information system (IS) is a formal, sociotechnical, organizational system designed to collect, process, store, and distribute information. From a sociotechnical perspective, information systems are composed by four components: task, people ...
s in order to understand hidden aspects of the systems. Cryptanalysis is used to breach
cryptographic Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or '' -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adve ...
security systems and gain access to the contents of
encrypted In cryptography, encryption is the process of encoding information. This process converts the original representation of the information, known as plaintext, into an alternative form known as ciphertext. Ideally, only authorized parties can decip ...
messages, even if the
cryptographic key A key in cryptography is a piece of information, usually a string of numbers or letters that are stored in a file, which, when processed through a cryptographic algorithm, can encode or decode cryptographic data. Based on the used method, the key c ...
is unknown. In addition to mathematical analysis of cryptographic algorithms, cryptanalysis includes the study of
side-channel attacks In computer security, a side-channel attack is any attack based on extra information that can be gathered because of the fundamental way a computer protocol or algorithm is Implementation#Computer science, implemented, rather than flaws in the d ...
that do not target weaknesses in the cryptographic algorithms themselves, but instead exploit weaknesses in their implementation. 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 the British
Bombe The bombe () was an electro-mechanical device used by British cryptologists to help decipher German Enigma-machine-encrypted secret messages during World War II. The US Navy and US Army later produced their own machines to the same functiona ...
s and
Colossus computer Colossus was a set of computers developed by British codebreakers in the years 1943–1945 to help in the cryptanalysis of the Lorenz cipher. Colossus used thermionic valves (vacuum tubes) to perform Boolean and counting operations. Colossus ...
s at
Bletchley Park Bletchley Park is an English country house and estate in Bletchley, Milton Keynes ( Buckinghamshire) that became the principal centre of Allied code-breaking during the Second World War. The mansion was constructed during the years following ...
in
World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
, to the mathematically advanced computerized schemes of the present. Methods for breaking modern
cryptosystem In cryptography, a cryptosystem is a suite of cryptographic algorithms needed to implement a particular security service, such as confidentiality (encryption). Typically, a cryptosystem consists of three algorithms: one for key generation, one for ...
s often involve solving carefully constructed problems in
pure mathematics Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications, ...
, the best-known being
integer factorization In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these factors are further restricted to prime numbers, the process is called prime factorization. When the numbers are suf ...
.


Overview

In
encryption In cryptography, encryption is the process of encoding information. This process converts the original representation of the information, known as plaintext, into an alternative form known as ciphertext. Ideally, only authorized parties can decip ...
, confidential information (called the ''"
plaintext In cryptography, plaintext usually means unencrypted information pending input into cryptographic algorithms, usually encryption algorithms. This usually refers to data that is transmitted or stored unencrypted. Overview With the advent of comp ...
"'') is sent securely to a recipient by the sender first converting it into an unreadable form (''"
ciphertext In cryptography, ciphertext or cyphertext is the result of encryption performed on plaintext using an algorithm, called a cipher. Ciphertext is also known as encrypted or encoded information because it contains a form of the original plaintext ...
"'') using an
encryption algorithm In cryptography, encryption is the process of encoding information. This process converts the original representation of the information, known as plaintext, into an alternative form known as ciphertext. Ideally, only authorized parties can decip ...
. The ciphertext is sent through an insecure channel to the recipient. The recipient decrypts the ciphertext by applying an inverse decryption algorithm, recovering the plaintext. To decrypt the ciphertext, the recipient requires a secret knowledge from the sender, usually a string of letters, numbers, or bits, called a ''
cryptographic key A key in cryptography is a piece of information, usually a string of numbers or letters that are stored in a file, which, when processed through a cryptographic algorithm, can encode or decode cryptographic data. Based on the used method, the key c ...
''. The concept is that even if an unauthorized person gets access to the ciphertext during transmission, without the secret key they cannot convert it back to plaintext. Encryption has been used throughout history to send important military, diplomatic and commercial messages, and today is very widely used in
computer networking A computer network is a set of computers sharing resources located on or provided by network nodes. The computers use common communication protocols over digital interconnections to communicate with each other. These interconnections are ma ...
to protect email and internet communication. The goal of cryptanalysis is for a third party, a
cryptanalyst Cryptanalysis (from the Greek ''kryptós'', "hidden", and ''analýein'', "to analyze") refers to the process of analyzing information systems in order to understand hidden aspects of the systems. Cryptanalysis is used to breach cryptographic sec ...
, to gain as much information as possible about the original (''"
plaintext In cryptography, plaintext usually means unencrypted information pending input into cryptographic algorithms, usually encryption algorithms. This usually refers to data that is transmitted or stored unencrypted. Overview With the advent of comp ...
"''), attempting to “break” the encryption to read the ciphertext and learning the secret key so future messages can be decrypted and read. A mathematical technique to do this is called a “‘’cryptographic attack’’”Cryptographic attacks can be characterized in a number of ways:


Amount of information available to the attacker

Attacks can be classified based on what type of information the attacker has available. As a basic starting point it is normally assumed that, for the purposes of analysis, the general
algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specificat ...
is known; this is Shannon's Maxim "the enemy knows the system" – in its turn, equivalent to
Kerckhoffs' principle Kerckhoffs's principle (also called Kerckhoffs's desideratum, assumption, axiom, doctrine or law) of cryptography was stated by Dutch-born cryptographer Auguste Kerckhoffs in the 19th century. The principle holds that a cryptosystem should be ...
. This is a reasonable assumption in practice – throughout history, there are countless examples of secret algorithms falling into wider knowledge, variously through
espionage Espionage, spying, or intelligence gathering is the act of obtaining secret or confidential information (intelligence) from non-disclosed sources or divulging of the same without the permission of the holder of the information for a tangibl ...
,
betrayal Betrayal is the breaking or violation of a presumptive contract, trust, or confidence that produces moral and psychological conflict within a relationship amongst individuals, between organizations or between individuals and organizations. Ofte ...
and
reverse engineering Reverse engineering (also known as backwards engineering or back engineering) is a process or method through which one attempts to understand through deductive reasoning how a previously made device, process, system, or piece of software accompli ...
. (And on occasion, ciphers have been broken through pure deduction; for example, the German
Lorenz cipher The Lorenz SZ40, SZ42a and SZ42b were German rotor stream cipher machines used by the German Army during World War II. They were developed by C. Lorenz AG in Berlin. The model name ''SZ'' was derived from ''Schlüssel-Zusatz'', meaning ''cipher ...
and the Japanese
Purple code In the history of cryptography, the "System 97 Typewriter for European Characters" (九七式欧文印字機) or "Type B Cipher Machine", codenamed Purple by the United States, was an encryption machine used by the Japanese Foreign Office fr ...
, and a variety of classical schemes): * ''
Ciphertext-only In cryptography, a ciphertext-only attack (COA) or known ciphertext attack is an attack model for cryptanalysis where the attacker is assumed to have access only to a set of ciphertexts. While the attacker has no channel providing access to the p ...
'': the cryptanalyst has access only to a collection of
ciphertext In cryptography, ciphertext or cyphertext is the result of encryption performed on plaintext using an algorithm, called a cipher. Ciphertext is also known as encrypted or encoded information because it contains a form of the original plaintext ...
s or
codetext In cryptology, a code is a method used to encrypt a message that operates at the level of meaning; that is, words or phrases are converted into something else. A code might transform "change" into "CVGDK" or "cocktail lounge". The U.S. Nat ...
s. * '' Known-plaintext'': the attacker has a set of ciphertexts to which they know the corresponding
plaintext In cryptography, plaintext usually means unencrypted information pending input into cryptographic algorithms, usually encryption algorithms. This usually refers to data that is transmitted or stored unencrypted. Overview With the advent of comp ...
. * '' Chosen-plaintext'' ('' chosen-ciphertext''): the attacker can obtain the ciphertexts (plaintexts) corresponding to an arbitrary set of plaintexts (ciphertexts) of their own choosing. * '' Adaptive chosen-plaintext'': like a chosen-plaintext attack, except the attacker can choose subsequent plaintexts based on information learned from previous encryptions, similarly to the ''
Adaptive chosen ciphertext attack An adaptive chosen-ciphertext attack (abbreviated as CCA2) is an interactive form of chosen-ciphertext attack in which an attacker first sends a number of ciphertexts to be decrypted chosen adaptively, and then uses the results to distinguish a tar ...
''. * ''
Related-key attack 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 k ...
'': Like a chosen-plaintext attack, except the attacker can obtain ciphertexts encrypted under two different keys. The keys are unknown, but the relationship between them is known; for example, two keys that differ in the one bit.


Computational resources required

Attacks can also be characterised by the resources they require. Those resources include: * Time – the number of ''computation steps'' (e.g., test encryptions) which must be performed. * Memory – the amount of ''storage'' required to perform the attack. * Data – the quantity and type of ''plaintexts and ciphertexts'' required for a particular approach. It's sometimes difficult to predict these quantities precisely, especially when the attack isn't practical to actually implement for testing. But academic cryptanalysts tend to provide at least the estimated ''order of magnitude'' of their attacks' difficulty, saying, for example, "SHA-1 collisions now 252."
Bruce Schneier Bruce Schneier (; born January 15, 1963) is an American cryptographer, computer security professional, privacy specialist, and writer. Schneier is a Lecturer in Public Policy at the Harvard Kennedy School and a Fellow at the Berkman Klein Cente ...
notes that even computationally impractical attacks can be considered breaks: "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."


Partial breaks

The results of cryptanalysis can also vary in usefulness. Cryptographer
Lars Knudsen Lars Ramkilde Knudsen (born 21 February 1962) is a Danish researcher in cryptography, particularly interested in the design and analysis of block ciphers, hash functions and message authentication codes (MACs). Academic After some early work ...
(1998) classified various types of attack on
block cipher In cryptography, a block cipher is a deterministic algorithm operating on fixed-length groups of bits, called ''blocks''. Block ciphers are specified cryptographic primitive, elementary components in the design of many cryptographic protocols and ...
s according to the amount and quality of secret information that was discovered: * ''Total break'' – the attacker deduces the secret
key Key or The Key may refer to: Common meanings * Key (cryptography), a piece of information that controls the operation of a cryptography algorithm * Key (lock), device used to control access to places or facilities restricted by a lock * Key (map ...
. * ''Global deduction'' – the attacker discovers a functionally equivalent
algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specificat ...
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 In information theory, the information content, self-information, surprisal, or Shannon information is a basic quantity derived from the probability of a particular event occurring from a random variable. It can be thought of as an alternative wa ...
about plaintexts (or ciphertexts) not previously known. * ''Distinguishing algorithm'' – the attacker can distinguish the cipher from a random
permutation In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or proc ...
. Academic attacks are often against weakened versions of a cryptosystem, such as a block cipher or hash function with some rounds removed. Many, but not all, attacks become exponentially more difficult to execute as rounds are added to a cryptosystem, so it's possible for the full cryptosystem to be strong even though reduced-round variants are weak. Nonetheless, partial breaks that come close to breaking the original cryptosystem may mean that a full break will follow; the successful attacks on
DES Des is a masculine given name, mostly a short form (hypocorism) of Desmond. People named Des include: People * Des Buckingham, English football manager * Des Corcoran, (1928–2004), Australian politician * Des Dillon (disambiguation), sever ...
, MD5, and
SHA-1 In cryptography, SHA-1 (Secure Hash Algorithm 1) is a cryptographically broken but still widely used hash function which takes an input and produces a 160-bit (20-byte) hash value known as a message digest – typically rendered as 40 hexadecima ...
were all preceded by attacks on weakened versions. In academic cryptography, a ''weakness'' or a ''break'' in a scheme is usually defined quite conservatively: it might require impractical amounts of time, memory, or known plaintexts. It also might require the attacker be able to do things many real-world attackers can't: for example, the attacker may need to choose particular plaintexts to be encrypted or even to ask for plaintexts to be encrypted using several keys related to the secret key. Furthermore, it might only reveal a small amount of information, enough to prove the cryptosystem imperfect but too little to be useful to real-world attackers. Finally, an attack might only apply to a weakened version of cryptographic tools, like a reduced-round block cipher, as a step towards breaking the full system.


History

Cryptanalysis has
coevolved In biology, coevolution occurs when two or more species reciprocally affect each other's evolution through the process of natural selection. The term sometimes is used for two traits in the same species affecting each other's evolution, as well ...
together with cryptography, and the contest can be traced through the
history of cryptography Cryptography, the use of codes and ciphers to protect secrets, began thousands of years ago. Until recent decades, it has been the story of what might be called classical cryptography — that is, of methods of encryption that use pen and paper, ...
—new
cipher In cryptography, a cipher (or cypher) is an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a procedure. An alternative, less common term is ''encipherment''. To encipher or encode i ...
s 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: secure cryptography requires design against possible cryptanalysis.


Classical ciphers

Although the actual word "''cryptanalysis''" is relatively recent (it was coined by
William Friedman William Frederick Friedman (September 24, 1891 – November 12, 1969) was a US Army cryptographer who ran the research division of the Army's Signal Intelligence Service (SIS) in the 1930s, and parts of its follow-on services into the 1950s. In ...
in 1920), methods for breaking
codes In communications and information processing, code is a system of rules to convert information—such as a letter, word, sound, image, or gesture—into another form, sometimes shortened or secret, for communication through a communication ...
and
cipher In cryptography, a cipher (or cypher) is an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a procedure. An alternative, less common term is ''encipherment''. To encipher or encode i ...
s are much older. David Kahn notes in ''
The Codebreakers ''The Codebreakers – The Story of Secret Writing'' () is a book by David Kahn, published in 1967, comprehensively chronicling the history of cryptography from ancient Egypt to the time of its writing. The United States government attempted to h ...
'' that
Arab scholars This is a list of Arab scientists and scholars from the Muslim World, including Al-Andalus (Spain), who lived from Ancient history, antiquity up until the beginning of the Modern era, modern age, consisting primarily of scholars during the Midd ...
were the first people to systematically document cryptanalytic methods. The first known recorded explanation of cryptanalysis was given by
Al-Kindi Abū Yūsuf Yaʻqūb ibn ʼIsḥāq aṣ-Ṣabbāḥ al-Kindī (; ar, أبو يوسف يعقوب بن إسحاق الصبّاح الكندي; la, Alkindus; c. 801–873 AD) was an Arab Muslim philosopher, polymath, mathematician, physician ...
(c. 801–873, also known as "Alkindus" in Europe), a 9th-century Arab
polymath A polymath ( el, πολυμαθής, , "having learned much"; la, homo universalis, "universal human") is an individual whose knowledge spans a substantial number of subjects, known to draw on complex bodies of knowledge to solve specific pro ...
, in ''Risalah fi Istikhraj al-Mu'amma'' (''A Manuscript on Deciphering Cryptographic Messages''). This treatise contains the first description of the method of
frequency analysis In cryptanalysis, frequency analysis (also known as counting letters) is the study of the frequency of letters or groups of letters in a ciphertext. The method is used as an aid to breaking classical ciphers. Frequency analysis is based on t ...
.Ibrahim A. Al-Kadi (April 1992), "The origins of cryptology: The Arab contributions”, '' Cryptologia'' 16 (2): 97–126 Al-Kindi is thus regarded as the first codebreaker in history. His breakthrough work was influenced by
Al-Khalil Hebron ( ar, الخليل or ; he, חֶבְרוֹן ) is a Palestinian. city in the southern West Bank, south of Jerusalem. Nestled in the Judaean Mountains, it lies above sea level. The second-largest city in the West Bank (after East J ...
(717–786), who wrote the ''Book of Cryptographic Messages'', which contains the first use of permutations and combinations to list all possible
Arabic Arabic (, ' ; , ' or ) is a Semitic languages, Semitic language spoken primarily across the Arab world.Semitic languages: an international handbook / edited by Stefan Weninger; in collaboration with Geoffrey Khan, Michael P. Streck, Janet C ...
words with and without vowels. Frequency analysis is the basic tool for breaking most
classical cipher In cryptography, a classical cipher is a type of cipher that was used historically but for the most part, has fallen into disuse. In contrast to modern cryptographic algorithms, most classical ciphers can be practically computed and solved by hand. ...
s. In natural languages, certain letters of the
alphabet An alphabet is a standardized set of basic written graphemes (called letters) that represent the phonemes of certain spoken languages. Not all writing systems represent language in this way; in a syllabary, each character represents a syll ...
appear more often than others; in
English English usually refers to: * English language * English people English may also refer to: Peoples, culture, and language * ''English'', an adjective for something of, from, or related to England ** English national ide ...
, " E" is likely to be the most common letter in any sample of
plaintext In cryptography, plaintext usually means unencrypted information pending input into cryptographic algorithms, usually encryption algorithms. This usually refers to data that is transmitted or stored unencrypted. Overview With the advent of comp ...
. 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 Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
. For example, in a
simple substitution cipher In cryptography, a substitution cipher is a method of encrypting in which units of plaintext are replaced with the ciphertext, in a defined manner, with the help of a key; the "units" may be single letters (the most common), pairs of letters, trip ...
(where each letter is simply replaced with another), the most frequent letter in the
ciphertext In cryptography, ciphertext or cyphertext is the result of encryption performed on plaintext using an algorithm, called a cipher. Ciphertext is also known as encrypted or encoded information because it contains a form of the original plaintext ...
would be a likely candidate for "E". Frequency analysis of such a cipher is therefore relatively easy, provided that the ciphertext is long enough to give a reasonably representative count of the letters of the alphabet that it contains. Al-Kindi's invention of the frequency analysis technique for breaking monoalphabetic
substitution cipher In cryptography, a substitution cipher is a method of encrypting in which units of plaintext are replaced with the ciphertext, in a defined manner, with the help of a key; the "units" may be single letters (the most common), pairs of letters, trip ...
s was the most significant cryptanalytic advance until World War II. Al-Kindi's ''Risalah fi Istikhraj al-Mu'amma'' described the first cryptanalytic techniques, including some for polyalphabetic ciphers, cipher classification, Arabic phonetics and syntax, and most importantly, gave the first descriptions on frequency analysis. He also covered methods of encipherments, cryptanalysis of certain encipherments, and
statistical analysis Statistical inference is the process of using data analysis to infer properties of an underlying distribution of probability.Upton, G., Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP. . Inferential statistical analysis infers propertie ...
of letters and letter combinations in Arabic. An important contribution of
Ibn Adlan ʻAfīf al-Dīn ʻAlī ibn ʻAdlān al-Mawsilī ( ar, عفيف لدين علي بن عدلان الموصلي ; 1187–1268 CE), born in Mosul, was an Arab cryptologist, linguist and poet who is known for his early contributions to cryptanalysis ...
(1187–1268) was on
sample size Sample size determination is the act of choosing the number of observations or Replication (statistics), replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make stat ...
for use of frequency analysis. In Europe,
Italian Italian(s) may refer to: * Anything of, from, or related to the people of Italy over the centuries ** Italians, an ethnic group or simply a citizen of the Italian Republic or Italian Kingdom ** Italian language, a Romance language *** Regional Ita ...
scholar
Giambattista della Porta Giambattista della Porta (; 1535 – 4 February 1615), also known as Giovanni Battista Della Porta, was an Italian scholar, polymath and playwright who lived in Naples at the time of the Renaissance, Scientific Revolution and Reformation. Giamba ...
(1535–1615) was the author of a seminal work on cryptanalysis, ''
De Furtivis Literarum Notis ''De Furtivis Literarum Notis'' (''On the Secret Symbols of Letters'') is a 1563 book on cryptography written by Giambattista della Porta. The book includes three sets of cypher discs for coding and decoding messages and a substitution cipher imp ...
''. Successful cryptanalysis has undoubtedly influenced history; the ability to read the presumed-secret thoughts and plans of others can be a decisive advantage. For example, in England in 1587,
Mary, Queen of Scots Mary, Queen of Scots (8 December 1542 – 8 February 1587), also known as Mary Stuart or Mary I of Scotland, was Queen of Scotland from 14 December 1542 until her forced abdication in 1567. The only surviving legitimate child of James V of Scot ...
was tried and executed for
treason Treason is the crime of attacking a state authority to which one owes allegiance. This typically includes acts such as participating in a war against one's native country, attempting to overthrow its government, spying on its military, its diplo ...
as a result of her involvement in three plots to assassinate
Elizabeth I of England Elizabeth I (7 September 153324 March 1603) was List of English monarchs, Queen of England and List of Irish monarchs, Ireland from 17 November 1558 until her death in 1603. Elizabeth was the last of the five House of Tudor monarchs and is ...
. The plans came to light after her coded correspondence with fellow conspirators was deciphered by
Thomas Phelippes Thomas Phelippes (1556–1625), also known as Thomas Phillips was a linguist, who was employed as a forger and intelligence gatherer. He served mainly under Sir Francis Walsingham, in the time of Elizabeth I, and most notably deciphered the code ...
. In Europe during the 15th and 16th centuries, the idea of a polyalphabetic substitution cipher was developed, among others by the French diplomat
Blaise de Vigenère Blaise de Vigenère (5 April 1523 – 19 February 1596) () was a French diplomat, cryptographer, translator and alchemist. Biography Vigenère was born into a respectable family in the village of Saint-Pourçain. His mother, Jean, arrang ...
(1523–96). For some three centuries, the
Vigenère cipher The Vigenère cipher () is a method of encryption, encrypting alphabetic text by using a series of interwoven Caesar ciphers, based on the letters of a keyword. It employs a form of polyalphabetic cipher, polyalphabetic substitution. First desc ...
, which uses a repeating key to select different encryption alphabets in rotation, was considered to be completely secure (''le chiffre indéchiffrable''—"the indecipherable cipher"). Nevertheless,
Charles Babbage Charles Babbage (; 26 December 1791 – 18 October 1871) was an English polymath. A mathematician, philosopher, inventor and mechanical engineer, Babbage originated the concept of a digital programmable computer. Babbage is considered ...
(1791–1871) and later, independently,
Friedrich Kasiski Major Friedrich Wilhelm Kasiski (29 November 1805 – 22 May 1881) was a German infantry officer, cryptographer and archeologist. Kasiski was born in Schlochau, Kingdom of Prussia (now Człuchów, Poland). Military service Kasiski enlisted in ...
(1805–81) succeeded in breaking this cipher. During
World War I World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fightin ...
, inventors in several countries developed rotor cipher machines such as
Arthur Scherbius Arthur Scherbius (30 October 1878 – 13 May 1929) was a German electrical engineer who invented the mechanical cipher Enigma machine. He patented the invention and later sold the machine under the brand name Enigma. Scherbius offered uneq ...
'
Enigma Enigma may refer to: *Riddle, someone or something that is mysterious or puzzling Biology *ENIGMA, a class of gene in the LIM domain Computing and technology * Enigma (company), a New York-based data-technology startup * Enigma machine, a family ...
, in an attempt to minimise the repetition that had been exploited to break the Vigenère system.


Ciphers from World War I and World War II

In
World War I World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fightin ...
, the breaking of the Zimmermann Telegram was instrumental in bringing the United States into the war. In
World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
, the
Allies An alliance is a relationship among people, groups, or states that have joined together for mutual benefit or to achieve some common purpose, whether or not explicit agreement has been worked out among them. Members of an alliance are called ...
benefitted enormously from their joint success cryptanalysis of the German ciphers – including the Enigma machine and the
Lorenz cipher The Lorenz SZ40, SZ42a and SZ42b were German rotor stream cipher machines used by the German Army during World War II. They were developed by C. Lorenz AG in Berlin. The model name ''SZ'' was derived from ''Schlüssel-Zusatz'', meaning ''cipher ...
– and Japanese ciphers, particularly 'Purple' and
JN-25 The vulnerability of Japanese naval codes and ciphers was crucial to the conduct of World War II, and had an important influence on foreign relations between Japan and the west in the years leading up to the war as well. Every Japanese code was e ...
. 'Ultra' intelligence has been credited with everything between shortening the end of the European war by up to two years, to determining the eventual result. The war in the Pacific was similarly helped by 'Magic' intelligence. Cryptanalysis of enemy messages played a significant part in the
Allied An alliance is a relationship among people, groups, or states that have joined together for mutual benefit or to achieve some common purpose, whether or not explicit agreement has been worked out among them. Members of an alliance are called ...
victory in World War II. F. W. Winterbotham, quoted the western Supreme Allied Commander,
Dwight D. Eisenhower Dwight David "Ike" Eisenhower (born David Dwight Eisenhower; ; October 14, 1890 – March 28, 1969) was an American military officer and statesman who served as the 34th president of the United States from 1953 to 1961. During World War II, ...
, at the war's end as describing
Ultra adopted by British military intelligence in June 1941 for wartime signals intelligence obtained by breaking high-level encrypted enemy radio and teleprinter communications at the Government Code and Cypher School (GC&CS) at Bletchley Park. '' ...
intelligence as having been "decisive" to Allied victory. Sir Harry Hinsley, official historian of British Intelligence in World War II, made a similar assessment about Ultra, saying that it shortened the war "by not less than two years and probably by four years"; moreover, he said that in the absence of Ultra, it is uncertain how the war would have ended. In practice, frequency analysis relies as much on
linguistic Linguistics is the scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of language, particularly its nature and structure. Linguis ...
knowledge as it does on statistics, but as ciphers became more complex,
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
became more important in cryptanalysis. This change was particularly evident before and during
World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
, where efforts to crack
Axis An axis (plural ''axes'') is an imaginary line around which an object rotates or is symmetrical. Axis may also refer to: Mathematics * Axis of rotation: see rotation around a fixed axis * Axis (mathematics), a designator for a Cartesian-coordinat ...
ciphers required new levels of mathematical sophistication. Moreover, automation was first applied to cryptanalysis in that era with the Polish Bomba device, the British
Bombe The bombe () was an electro-mechanical device used by British cryptologists to help decipher German Enigma-machine-encrypted secret messages during World War II. The US Navy and US Army later produced their own machines to the same functiona ...
, the use of
punched card A punched card (also punch card or punched-card) is a piece of stiff paper that holds digital data represented by the presence or absence of holes in predefined positions. Punched cards were once common in data processing applications or to di ...
equipment, and in the Colossus computers – the first electronic digital computers to be controlled by a program.


Indicator

With reciprocal machine ciphers such as the
Lorenz cipher The Lorenz SZ40, SZ42a and SZ42b were German rotor stream cipher machines used by the German Army during World War II. They were developed by C. Lorenz AG in Berlin. The model name ''SZ'' was derived from ''Schlüssel-Zusatz'', meaning ''cipher ...
and the Enigma machine used by
Nazi Germany Nazi Germany (lit. "National Socialist State"), ' (lit. "Nazi State") for short; also ' (lit. "National Socialist Germany") (officially known as the German Reich from 1933 until 1943, and the Greater German Reich from 1943 to 1945) was ...
during
World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
, each message had its own key. Usually, the transmitting operator informed the receiving operator of this message key by transmitting some plaintext and/or ciphertext before the enciphered message. This is termed the ''indicator'', as it indicates to the receiving operator how to set his machine to decipher the message. Poorly designed and implemented indicator systems allowed first
Polish cryptographers Polish may refer to: * Anything from or related to Poland, a country in Europe * Polish language * Poles Poles,, ; singular masculine: ''Polak'', singular feminine: ''Polka'' or Polish people, are a West Slavic nation and ethnic group, w ...
and then the British cryptographers at
Bletchley Park Bletchley Park is an English country house and estate in Bletchley, Milton Keynes ( Buckinghamshire) that became the principal centre of Allied code-breaking during the Second World War. The mansion was constructed during the years following ...
to break the Enigma cipher system. Similar poor indicator systems allowed the British to identify ''depths'' that led to the diagnosis of the Lorenz SZ40/42 cipher system, and the comprehensive breaking of its messages without the cryptanalysts seeing the cipher machine.


Depth

Sending two or more messages with the same key is an insecure process. To a cryptanalyst the messages are then said to be ''"in depth."'' This may be detected by the messages having the same ''
indicator Indicator may refer to: Biology * Environmental indicator of environmental health (pressures, conditions and responses) * Ecological indicator of ecosystem health (ecological processes) * Health indicator, which is used to describe the health o ...
'' by which the sending operator informs the receiving operator about the key generator initial settings for the message. Generally, the cryptanalyst may benefit from lining up identical enciphering operations among a set of messages. For example, the
Vernam cipher Vernam is a surname. Notable people with the surname include: *Charles Vernam (born 1996), English professional footballer *Gilbert Vernam (1890–1960), invented an additive polyalphabetic stream cipher and later co-invented an automated one-time ...
enciphers by bit-for-bit combining plaintext with a long key using the "
exclusive or Exclusive or or exclusive disjunction is a logical operation that is true if and only if its arguments differ (one is true, the other is false). It is symbolized by the prefix operator J and by the infix operators XOR ( or ), EOR, EXOR, , ...
" operator, which is also known as " modulo-2 addition" (symbolized by ⊕ ): ::::Plaintext ⊕ Key = Ciphertext Deciphering combines the same key bits with the ciphertext to reconstruct the plaintext: ::::Ciphertext ⊕ Key = Plaintext (In modulo-2 arithmetic, addition is the same as subtraction.) When two such ciphertexts are aligned in depth, combining them eliminates the common key, leaving just a combination of the two plaintexts: ::::Ciphertext1 ⊕ Ciphertext2 = Plaintext1 ⊕ Plaintext2 The individual plaintexts can then be worked out linguistically by trying ''probable words'' (or phrases), also known as ''"cribs,"'' at various locations; a correct guess, when combined with the merged plaintext stream, produces intelligible text from the other plaintext component: ::::(Plaintext1 ⊕ Plaintext2) ⊕ Plaintext1 = Plaintext2 The recovered fragment of the second plaintext can often be extended in one or both directions, and the extra characters can be combined with the merged plaintext stream to extend the first plaintext. Working back and forth between the two plaintexts, using the intelligibility criterion to check guesses, the analyst may recover much or all of the original plaintexts. (With only two plaintexts in depth, the analyst may not know which one corresponds to which ciphertext, but in practice this is not a large problem.) When a recovered plaintext is then combined with its ciphertext, the key is revealed: ::::Plaintext1 ⊕ Ciphertext1 = Key Knowledge of a key then allows the analyst to read other messages encrypted with the same key, and knowledge of a set of related keys may allow cryptanalysts to diagnose the system used for constructing them.


Development of modern cryptography

Governments have long recognized the potential benefits of cryptanalysis for
intelligence Intelligence has been defined in many ways: the capacity for abstraction, logic, understanding, self-awareness, learning, emotional knowledge, reasoning, planning, creativity, critical thinking, and problem-solving. More generally, it can b ...
, both military and diplomatic, and established dedicated organizations devoted to breaking the codes and ciphers of other nations, for example,
GCHQ Government Communications Headquarters, commonly known as GCHQ, is an intelligence and security organisation responsible for providing signals intelligence (SIGINT) and information assurance (IA) to the government and armed forces of the Unit ...
and the
NSA The National Security Agency (NSA) is a national-level intelligence agency of the United States Department of Defense, under the authority of the Director of National Intelligence (DNI). The NSA is responsible for global monitoring, collecti ...
, organizations which are still very active today. Even though computation was used to great effect in the
cryptanalysis of the Lorenz cipher Cryptanalysis of the Lorenz cipher was the process that enabled the British to read high-level German army messages during World War II. The British Government Code and Cypher School (GC&CS) at Bletchley Park decrypted many communications betwee ...
and other systems during World War II, it also made possible new methods of cryptography
orders of magnitude An order of magnitude is an approximation of the logarithm of a value relative to some contextually understood reference value, usually 10, interpreted as the base of the logarithm and the representative of values of magnitude one. Logarithmic dis ...
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: Kahn goes on to mention increased opportunities for interception,
bugging A covert listening device, more commonly known as a bug or a wire, is usually a combination of a miniature radio transmitter with a microphone. The use of bugs, called bugging, or wiretapping is a common technique in surveillance, espionage and ...
,
side channel attack In computer security, a side-channel attack is any attack based on extra information that can be gathered because of the fundamental way a computer protocol or algorithm is implemented, rather than flaws in the design of the protocol or algorit ...
s, and
quantum computers Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though ...
as replacements for the traditional means of cryptanalysis. In 2010, former NSA technical director Brian Snow said that both academic and government cryptographers are "moving very slowly forward in a mature field." However, any postmortems for cryptanalysis may be premature. While the effectiveness of cryptanalytic methods employed by intelligence agencies remains unknown, many serious attacks against both academic and practical cryptographic primitives have been published in the modern era of computer cryptography: * The
block cipher In cryptography, a block cipher is a deterministic algorithm operating on fixed-length groups of bits, called ''blocks''. Block ciphers are specified cryptographic primitive, elementary components in the design of many cryptographic protocols and ...
Madryga In cryptography, Madryga is a block cipher published in 1984 by W. E. Madryga. It was designed to be easy and efficient for implementation in software. Serious weaknesses have since been found in the algorithm, but it was one of the first encrypti ...
, proposed in 1984 but not widely used, was found to be susceptible to
ciphertext-only attack In cryptography, a ciphertext-only attack (COA) or known ciphertext attack is an attack model for cryptanalysis where the attacker is assumed to have access only to a set of ciphertexts. While the attacker has no channel providing access to the pl ...
s in 1998. * FEAL-4, proposed as a replacement for the
DES Des is a masculine given name, mostly a short form (hypocorism) of Desmond. People named Des include: People * Des Buckingham, English football manager * Des Corcoran, (1928–2004), Australian politician * Des Dillon (disambiguation), sever ...
standard encryption algorithm but not widely used, was demolished by a spate of attacks from the academic community, many of which are entirely practical. * The A5/1,
A5/2 A5/2 is a stream cipher used to provide voice privacy in the GSM cellular telephone protocol. It was designed in 1992-1993 (finished March 1993) as a replacement for the relatively stronger (but still weak) A5/1, to allow the GSM standard to b ...
, CMEA, and
DECT Digital enhanced cordless telecommunications (Digital European cordless telecommunications), usually known by the acronym DECT, is a standard primarily used for creating cordless telephone systems. It originated in Europe, where it is the common ...
systems used in
mobile Mobile may refer to: Places * Mobile, Alabama, a U.S. port city * Mobile County, Alabama * Mobile, Arizona, a small town near Phoenix, U.S. * Mobile, Newfoundland and Labrador Arts, entertainment, and media Music Groups and labels * Mobile ( ...
and wireless phone technology can all be broken in hours, minutes or even in real-time using widely available computing equipment. * Brute-force keyspace search has broken some real-world ciphers and applications, including single-DES (see
EFF DES cracker In cryptography, the EFF DES cracker (nicknamed "Deep Crack") is a machine built by the Electronic Frontier Foundation (EFF) in 1998, to perform a brute force search of the Data Encryption Standard (DES) cipher's key space – that is, to decr ...
), 40-bit "export-strength" cryptography, and the DVD Content Scrambling System. * In 2001,
Wired Equivalent Privacy Wired Equivalent Privacy (WEP) was a security algorithm for 802.11 wireless networks. Introduced as part of the original IEEE 802.11 standard ratified in 1997, its intention was to provide data confidentiality comparable to that of a traditional wi ...
(WEP), a protocol used to secure
Wi-Fi Wi-Fi () is a family of wireless network protocols, based on the IEEE 802.11 family of standards, which are commonly used for local area networking of devices and Internet access, allowing nearby digital devices to exchange data by radio wave ...
wireless network A wireless network is a computer network that uses wireless data connections between network nodes. Wireless networking is a method by which homes, telecommunications networks and business installations avoid the costly process of introducing c ...
s, was shown to be breakable in practice because of a weakness in the
RC4 In cryptography, RC4 (Rivest Cipher 4, also known as ARC4 or ARCFOUR, meaning Alleged RC4, see below) is a stream cipher. While it is remarkable for its simplicity and speed in software, multiple vulnerabilities have been discovered in RC4, ren ...
cipher and aspects of the WEP design that made
related-key attack 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 k ...
s practical. WEP was later replaced by
Wi-Fi Protected Access Wi-Fi Protected Access (WPA), Wi-Fi Protected Access II (WPA2), and Wi-Fi Protected Access 3 (WPA3) are the three security and security certification programs developed after 2000 by the Wi-Fi Alliance to secure wireless computer networks. The All ...
. * In 2008, researchers conducted a proof-of-concept break of SSL using weaknesses in the MD5
hash function A hash function is any function that can be used to map data of arbitrary size to fixed-size values. The values returned by a hash function are called ''hash values'', ''hash codes'', ''digests'', or simply ''hashes''. The values are usually u ...
and certificate issuer practices that made it possible to exploit
collision attack In cryptography, a collision attack on a cryptographic hash tries to find two inputs producing the same hash value, i.e. a hash collision. This is in contrast to a preimage attack where a specific target hash value is specified. There are roughl ...
s on hash functions. The certificate issuers involved changed their practices to prevent the attack from being repeated. Thus, while the best modern ciphers may be far more resistant to cryptanalysis than the
Enigma Enigma may refer to: *Riddle, someone or something that is mysterious or puzzling Biology *ENIGMA, a class of gene in the LIM domain Computing and technology * Enigma (company), a New York-based data-technology startup * Enigma machine, a family ...
, cryptanalysis and the broader field of
information security Information security, sometimes shortened to InfoSec, is the practice of protecting information by mitigating information risks. It is part of information risk management. It typically involves preventing or reducing the probability of unauthorize ...
remain quite active.


Symmetric ciphers

*
Boomerang attack In cryptography, the boomerang attack is a method for the cryptanalysis of block ciphers based on differential cryptanalysis. The attack was published in 1999 by David Wagner, who used it to break the COCONUT98 cipher. The boomerang attack ...
*
Brute-force attack In cryptography, a brute-force attack consists of an attacker submitting many passwords or passphrases with the hope of eventually guessing correctly. The attacker systematically checks all possible passwords and passphrases until the correct ...
* Davies' attack *
Differential cryptanalysis Differential cryptanalysis is a general form of cryptanalysis applicable primarily to block ciphers, but also to stream ciphers and cryptographic hash functions. In the broadest sense, it is the study of how differences in information input can aff ...
*
Impossible differential cryptanalysis In cryptography, impossible differential cryptanalysis is a form of differential cryptanalysis for block ciphers. While ordinary differential cryptanalysis tracks differences that propagate through the cipher with greater than expected probability, ...
*
Improbable differential cryptanalysis Improbable describes something that has a low probability. It may also refer to * Improbable (company), a British company founded in 2012 * Improbable (novel), a 2005 science fiction thriller novel by Adam Fawer * Improbable (The X-Files), an e ...
*
Integral cryptanalysis In cryptography, integral cryptanalysis is a cryptanalytic attack that is particularly applicable to block ciphers based on substitution–permutation networks. It was originally designed by Lars Knudsen as a dedicated attack against Square, so ...
*
Linear cryptanalysis In cryptography, linear cryptanalysis is a general form of cryptanalysis based on finding affine approximations to the action of a cipher. Attacks have been developed for block ciphers and stream ciphers. Linear cryptanalysis is one of the two most ...
* Meet-in-the-middle attack *
Mod-n cryptanalysis In cryptography, mod ''n'' cryptanalysis is an cryptanalysis, attack applicable to block cipher, block and stream ciphers. It is a form of partitioning cryptanalysis that exploits unevenness in how the cipher operates over equivalence classes (cong ...
*
Related-key attack 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 k ...
* Sandwich attack *
Slide attack The slide attack is a form of cryptanalysis designed to deal with the prevailing idea that even weak ciphers can become very strong by increasing the number of rounds, which can ward off a differential attack. The slide attack works in such a way ...
*
XSL attack In cryptography, the ''eXtended Sparse Linearization'' (XSL) attack is a method of cryptanalysis for block ciphers. The attack was first published in 2002 by researchers Nicolas Courtois and Josef Pieprzyk. It has caused some controversy as it was ...


Asymmetric ciphers

Asymmetric cryptography Public-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a public key and a corresponding private key. Key pairs are generated with cryptographic alg ...
(or
public-key cryptography Public-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a public key and a corresponding private key. Key pairs are generated with cryptographic alg ...
) is cryptography that relies on using two (mathematically related) keys; one private, and one public. Such ciphers invariably rely on "hard"
mathematical problem A mathematical problem is a problem that can be represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the orbits of the planets in the solar system, or a problem of a more ...
s 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. 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 Diffie–Hellman key exchangeSynonyms of Diffie–Hellman key exchange include: * Diffie–Hellman–Merkle key exchange * Diffie–Hellman key agreement * Diffie–Hellman key establishment * Diffie–Hellman key negotiation * Exponential key exc ...
scheme depends on the difficulty of calculating the
discrete logarithm In mathematics, for given real numbers ''a'' and ''b'', the logarithm log''b'' ''a'' is a number ''x'' such that . Analogously, in any group ''G'', powers ''b'k'' can be defined for all integers ''k'', and the discrete logarithm log''b' ...
. In 1983,
Don Coppersmith Don Coppersmith (born 1950) is a cryptographer and mathematician. He was involved in the design of the Data Encryption Standard block cipher at IBM, particularly the design of the S-boxes, strengthening them against differential cryptanalysis ...
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 In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these factors are further restricted to prime numbers, the process is called prime factorization. When the numbers are suf ...
– a breakthrough in factoring would impact the security of RSA. 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 Moore's law is the observation that the number of transistors in a dense integrated circuit (IC) doubles about every two years. Moore's law is an observation and projection of a historical trend. Rather than a law of physics, it is an empir ...
predicts that computer speeds will continue to increase. Factoring techniques may continue to 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 In cryptography, key size, key length, or key space refer to the number of bits in a key used by a cryptographic algorithm (such as a cipher). Key length defines the upper-bound on an algorithm's security (i.e. a logarithmic measure of the fastest ...
for RSA. Numbers with several hundred digits were still considered too hard to factor in 2005, though methods will probably continue to improve over time, requiring key size to keep pace or other methods such as
elliptic curve cryptography Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys compared to non-EC cryptography (based on plain Galois fields) to provide e ...
to be used. 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 Public-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a public key and a corresponding private key. Key pairs are generated with cryptographic alg ...
.


Attacking cryptographic hash systems

*
Birthday attack A birthday attack is a type of cryptographic attack that exploits the mathematics behind the birthday problem in probability theory. This attack can be used to abuse communication between two or more parties. The attack depends on the higher likeli ...
*
Hash function security summary This article summarizes publicly known cryptanalysis, attacks against cryptographic hash functions. Note that not all entries may be up to date. For a summary of other hash function parameters, see comparison of cryptographic hash functions. Tabl ...
*
Rainbow table A rainbow table is an efficient way to store data that has been computed in advance to facilitate cracking passwords. To protect stored passwords from compromise in case of a data breach, organizations avoid storing them directly, instead transfo ...


Side-channel attacks

*
Black-bag cryptanalysis In cryptography, black-bag cryptanalysis is a euphemism for the acquisition of cryptographic secrets via burglary, or other covert means – rather than mathematical or technical cryptanalytic attack. The term refers to the black bag of equipment ...
*
Man-in-the-middle attack In cryptography and computer security, a man-in-the-middle, monster-in-the-middle, machine-in-the-middle, monkey-in-the-middle, meddler-in-the-middle, manipulator-in-the-middle (MITM), person-in-the-middle (PITM) or adversary-in-the-middle (AiTM) ...
*
Power analysis Power analysis is a form of side channel attack in which the attacker studies the power consumption of a cryptographic hardware device. These attacks rely on basic physical properties of the device: semiconductor devices are governed by the ...
*
Replay attack A replay attack (also known as a repeat attack or playback attack) is a form of network attack in which valid data transmission is maliciously or fraudulently repeated or delayed. This is carried out either by the originator or by an adversary wh ...
*
Rubber-hose cryptanalysis In cryptography, rubber-hose cryptanalysis is a euphemism for the extraction of cryptographic secrets (e.g. the password to an encrypted file) from a person by coercion or torture—such as beating that person with a rubber hose, hence the na ...
*
Timing analysis Static timing analysis (STA) is a simulation method of computing the expected timing of a synchronous digital circuit without requiring a simulation of the full circuit. High-performance integrated circuits have traditionally been character ...


Quantum computing applications for cryptanalysis

Quantum computer Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though ...
s, which are still in the early phases of research, have potential use in cryptanalysis. For example,
Shor's Algorithm Shor's algorithm is a quantum algorithm, quantum computer algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor. On a quantum computer, to factor an integer N , Shor's algorithm ...
could factor large numbers in
polynomial time In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by ...
, in effect breaking some commonly used forms of public-key encryption. By using
Grover's algorithm In quantum computing, Grover's algorithm, also known as the quantum search algorithm, refers to a quantum algorithm for unstructured search that finds with high probability the unique input to a black box function that produces a particular output ...
on a quantum computer, brute-force key search can be made quadratically faster. However, this could be countered by doubling the key length.


See also

*
Economics of security The economics of information security addresses the economic aspects of privacy and computer security. Economics of information security includes models of the strictly rational “homo economicus” as well as behavioral economics. Economics of se ...
*
Global surveillance Global mass surveillance can be defined as the mass surveillance of entire populations across national borders. Its existence was not widely acknowledged by governments and the mainstream media until the global surveillance disclosures by Edwar ...
*
Information assurance Information assurance (IA) is the practice of assuring information and managing risks related to the use, processing, storage, and transmission of information. Information assurance includes protection of the integrity, availability, authenticity, n ...
, a term for information security often used in government *
Information security Information security, sometimes shortened to InfoSec, is the practice of protecting information by mitigating information risks. It is part of information risk management. It typically involves preventing or reducing the probability of unauthorize ...
, the overarching goal of most cryptography * National Cipher Challenge *
Security engineering Security engineering is the process of incorporating security controls into an information system so that the controls become an integral part of the system’s operational capabilities. It is similar to other systems engineering activities in tha ...
, the design of applications and protocols *
Security vulnerability Vulnerabilities are flaws in a computer system that weaken the overall security of the device/system. Vulnerabilities can be weaknesses in either the hardware itself, or the software that runs on the hardware. Vulnerabilities can be exploited by ...
; vulnerabilities can include cryptographic or other flaws *
Topics in cryptography The following outline is provided as an overview of and topical guide to cryptography: Cryptography (or cryptology) – practice and study of hiding information. Modern cryptography intersects the disciplines of mathematics, computer scienc ...
* Zendian Problem


Historic cryptanalysts

*
Conel Hugh O'Donel Alexander Conel Hugh O'Donel Alexander (19 April 1909 – 15 February 1974), known as Hugh Alexander and C. H. O'D. Alexander, was an Ireland, Irish-born United Kingdom, British cryptanalyst, chess player, and chess writer. He worked on the ...
*
Charles Babbage Charles Babbage (; 26 December 1791 – 18 October 1871) was an English polymath. A mathematician, philosopher, inventor and mechanical engineer, Babbage originated the concept of a digital programmable computer. Babbage is considered ...
* Lambros D. Callimahos *
Joan Clarke Joan Elisabeth Lowther Murray, MBE (''née'' Clarke; 24 June 1917 – 4 September 1996) was an English cryptanalyst and numismatist best known for her work as a code-breaker at Bletchley Park during the Second World War. Although she did not ...
*
Alastair Denniston Commander Alexander "Alastair" Guthrie Denniston (1 December 1881 – 1 January 1961) was a Scottish codebreaker in Room 40, deputy head of the Government Code and Cypher School (GC&CS) and hockey player. Denniston was appointed operational he ...
* Agnes Meyer Driscoll *
Elizebeth Friedman Elizebeth Smith Friedman (August 26, 1892 – October 31, 1980) was an American cryptanalyst and author who deciphered enemy codes in both World Wars and helped to solve international smuggling cases during Prohibition. Over the course of her ...
*
William F. Friedman William Frederick Friedman (September 24, 1891 – November 12, 1969) was a US Army cryptographer who ran the research division of the Army's Signal Intelligence Service (SIS) in the 1930s, and parts of its follow-on services into the 1950s. ...
*
Meredith Gardner Meredith Knox Gardner (October 20, 1912August 9, 2002) was an American linguist and codebreaker. Gardner worked in counter-intelligence, decoding Soviet intelligence traffic regarding espionage in the United States, in what came to be known as ...
*
Friedrich Kasiski Major Friedrich Wilhelm Kasiski (29 November 1805 – 22 May 1881) was a German infantry officer, cryptographer and archeologist. Kasiski was born in Schlochau, Kingdom of Prussia (now Człuchów, Poland). Military service Kasiski enlisted in ...
*
Al-Kindi Abū Yūsuf Yaʻqūb ibn ʼIsḥāq aṣ-Ṣabbāḥ al-Kindī (; ar, أبو يوسف يعقوب بن إسحاق الصبّاح الكندي; la, Alkindus; c. 801–873 AD) was an Arab Muslim philosopher, polymath, mathematician, physician ...
*
Dilly Knox Alfred Dillwyn "Dilly" Knox, CMG (23 July 1884 – 27 February 1943) was a British classics scholar and papyrologist at King's College, Cambridge and a codebreaker. As a member of the Room 40 codebreaking unit he helped decrypt the Zimm ...
*
Solomon Kullback Solomon Kullback (April 3, 1907August 5, 1994) was an American cryptanalyst and mathematician, who was one of the first three employees hired by William F. Friedman at the US Army's Signal Intelligence Service (SIS) in the 1930s, along with Frank ...
*
Marian Rejewski Marian Adam Rejewski (; 16 August 1905 – 13 February 1980) was a Polish mathematician and cryptologist who in late 1932 reconstructed the sight-unseen German military Enigma cipher machine, aided by limited documents obtained by French mili ...
*
Joseph Rochefort Joseph John Rochefort (May 12, 1900 – July 20, 1976) was an American naval officer and cryptanalyst. He was a major figure in the United States Navy's cryptographic and intelligence operations from 1925 to 1946, particularly in the Battle of M ...
, whose contributions affected the outcome of the
Battle of Midway The Battle of Midway was a major naval battle in the Pacific Theater of World War II that took place on 4–7 June 1942, six months after Japan's attack on Pearl Harbor and one month after the Battle of the Coral Sea. The U.S. Navy under Adm ...
*
Frank Rowlett Frank Byron Rowlett (May 2, 1908 – June 29, 1998) was an American cryptologist. Life and career Rowlett was born in Rose Hill, Lee County, Virginia and attended Emory & Henry College in Emory, Virginia. In 1929 he received a bachelor's d ...
*
Abraham Sinkov Abraham Sinkov (August 22, 1907 – January 19, 1998) was a US cryptanalyst. An early employee of the U.S. Army's Signals Intelligence Service, he held several leadership positions during World War II, transitioning to the new National Security A ...
* Giovanni Soro, the Renaissance's first outstanding cryptanalyst *
John Tiltman Brigadier John Hessell Tiltman, (25 May 1894 – 10 August 1982) was a British Army officer who worked in intelligence, often at or with the Government Code and Cypher School (GC&CS) starting in the 1920s. His intelligence work was largely conn ...
*
Alan Turing Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist. Turing was highly influential in the development of theoretical com ...
*
William T. Tutte William Thomas Tutte OC FRS FRSC (; 14 May 1917 – 2 May 2002) was an English and Canadian codebreaker and mathematician. During the Second World War, he made a brilliant and fundamental advance in cryptanalysis of the Lorenz cipher, a majo ...
*
John Wallis John Wallis (; la, Wallisius; ) was an English clergyman and mathematician who is given partial credit for the development of infinitesimal calculus. Between 1643 and 1689 he served as chief cryptographer for Parliament and, later, the royal ...
– 17th-century English mathematician * William Stone Weedon – worked with
Fredson Bowers Fredson Thayer Bowers (April 25, 1905 – April 11, 1991) was an American Bibliography, bibliographer and scholar of Textual criticism, textual editing. Life Bowers was a graduate of Brown University and Harvard University (Ph.D.). He taught at ...
in World War II * Herbert Yardley


References


Citations


Sources

*
Ibrahim A. Al-Kadi Ibrahim ( ar, إبراهيم, links=no ') is the Arabic name for Abraham, a Biblical patriarch and prophet in Islam. For the Islamic view of Ibrahim, see Abraham in Islam. Ibrahim may also refer to: * Ibrahim (name), a name (and list of people w ...
,"The origins of cryptology: The Arab contributions", '' Cryptologia'', 16(2) (April 1992) pp. 97–126. * Friedrich L. Bauer: "Decrypted Secrets". Springer 2002. * * * * * * Helen Fouché Gaines, "Cryptanalysis", 1939, Dover. * David Kahn, "
The Codebreakers ''The Codebreakers – The Story of Secret Writing'' () is a book by David Kahn, published in 1967, comprehensively chronicling the history of cryptography from ancient Egypt to the time of its writing. The United States government attempted to h ...
– The Story of Secret Writing", 1967. * Lars R. Knudsen: Contemporary Block Ciphers. Lectures on Data Security 1998: 105–126 * *
Abraham Sinkov Abraham Sinkov (August 22, 1907 – January 19, 1998) was a US cryptanalyst. An early employee of the U.S. Army's Signals Intelligence Service, he held several leadership positions during World War II, transitioning to the new National Security A ...
, ''Elementary Cryptanalysis: A Mathematical Approach'', Mathematical Association of America, 1966. *
Christopher Swenson Christopher is the English version of a Europe-wide name derived from the Greek name Χριστόφορος (''Christophoros'' or '' Christoforos''). The constituent parts are Χριστός (''Christós''), "Christ" or "Anointed", and φέρει ...
, Modern Cryptanalysis: Techniques for Advanced Code Breaking, * Friedman, William F., Military Cryptanalysis, Part I, * Friedman, William F., Military Cryptanalysis, Part II, * Friedman, William F., Military Cryptanalysis, Part III, Simpler Varieties of Aperiodic Substitution Systems, * Friedman, William F., Military Cryptanalysis, Part IV, Transposition and Fractionating Systems, * Friedman, William F. and Lambros D. Callimahos,
Military Cryptanalytics ''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''. It may also contain contributions by other cr ...
, Part I, Volume 1, * Friedman, William F. and Lambros D. Callimahos, Military Cryptanalytics, Part I, Volume 2, * Friedman, William F. and Lambros D. Callimahos, Military Cryptanalytics, Part II, Volume 1, * Friedman, William F. and Lambros D. Callimahos, Military Cryptanalytics, Part II, Volume 2, * * * * Transcript of a lecture given by Prof. Tutte at the
University of Waterloo The University of Waterloo (UWaterloo, UW, or Waterloo) is a public research university with a main campus in Waterloo, Ontario Waterloo is a city in the Canadian province of Ontario. It is one of three cities in the Regional Municipality ...
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Further reading

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External links


Basic Cryptanalysis
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List of tools for cryptanalysis on modern cryptography

Simon Singh's crypto corner

The National Museum of Computing

UltraAnvil tool for attacking simple substitution ciphers

How Alan Turing Cracked The Enigma Code
Imperial War Museums {{Authority control Cryptographic attacks Applied mathematics Arab inventions