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y document cryptanalytic methods 9 the first known recorded explanation of cryptanalysis was given by al kindi c 801 873 also known as alkindus in europe a 9th century arab polymath 10 11 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 12 al kindi is thus regarded as the first codebreaker in history 13 his breakthrough work was influenced by al khalil 717 786 who wrote the book of cryptographic messages which contains the first use of permutations and combinations to list all possible arabic words with and without vowels 14 frequency analysis is the basic tool for breaking most classical ciphers in natural languages certain letters of the alphabet appear more often 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 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 15 al kindi s invention of the frequency analysis technique for breaking monoalphabetic substitution ciphers 16 17 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 18 he also covered methods of encipherments cryptanalysis of certain encipherments and statistical analysis of letters and letter combinations in arabic 19 12 an important contribution of ibn adlan 1187 1268 was on sample size for use of frequency analysis 14 in europe italian scholar giambattista della porta 1535 1615 was the author of a seminal work on cryptanalysis de furtivis literarum notis 20 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 was tried and executed for treason as a result of her involvement in three plots to assassinate elizabeth i of england the plans came to light after her coded correspondence with fellow conspirators was deciphered by thomas phelippes 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 1523 96 21 for some three centuries the vigenère cipher 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 1791 1871 and later independently friedrich kasiski 1805 81 succeeded in breaking this cipher 22 during world war i inventors in several countries developed rotor cipher machines such as arthur scherbius enigma in an attempt to minimise the repetition that had been exploited to break the vigenère system 23 ciphers from world war i and world war ii edit see also cryptanalysis of the enigma and cryptanalysis of the lorenz cipher the decrypted zimmermann telegram 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 allies benefitted enormously from their joint success cryptanalysis of the german ciphers including the enigma machine and the lorenz cipher and japanese ciphers particularly purple and jn 25 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 24 cryptanalysis of enemy messages played a significant part in the allied victory in world war ii f w winterbotham quoted the western supreme allied commander dwight d eisenhower at the war s end as describing ultra intelligence as having been decisive to allied victory 25 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 26 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 before and 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 the british bombe the use of punched card equipment and in the colossus computers the first electronic digital computers to be controlled by a program 27 28 indicator edit with reciprocal machine ciphers such as the lorenz cipher and the enigma machine used by nazi germany during world war ii 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 29 poorly designed and implemented indicator systems allowed first polish cryptographers 30 and then the british cryptographers at bletchley park 31 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 32 depth edit 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 33 34 this may be detected by the messages having the same indicator by which the sending operator informs the receiving operator about the key generator initial settings for the message 35 generally the cryptanalyst may benefit from lining up identical enciphering operations among a set of messages for example the vernam cipher enciphers by bit for bit combining plaintext with a long key using the exclusive or 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 cyphertext1 cyphertext2 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 32 development of modern cryptography edit governments have long recognized the potential benefits of cryptanalysis for intelligence both military and diplomatic and established dedicated organizations devoted to breaking the codes and ciphers of other nations for example gchq and the nsa organizations which are still very active today the bombe replicated the action of several enigma machines wired together each of the rapidly rotating drums pictured above in a bletchley park museum mockup simulated the action of an enigma rotor even though computation was used to great effect in the cryptanalysis of the lorenz cipher and other systems during 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 citation needed the historian david kahn notes 36 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 s 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 kahn goes on to mention increased opportunities for interception bugging side channel attacks and quantum computers 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 37 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 38 the block cipher madryga proposed in 1984 but not widely used was found to be susceptible to ciphertext only attacks in 1998 feal 4 proposed as a replacement for the des 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 cmea and dect systems used in 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 40 bit export strength cryptography and the dvd content scramble system in 2001 wired equivalent privacy wep a protocol used to secure wi fi wireless networks was shown to be breakable in practice because of a weakness in the rc4 cipher and aspects of the wep design that made related key attacks practical wep was later replaced by wi fi protected access in 2008 researchers conducted a proof of concept break of ssl using weaknesses in the md5 hash function and certificate issuer practices that made it possible to exploit collision attacks 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 cryptanalysis and the broader field of information security remain quite active 39 symmetric ciphers edit boomerang attack brute force attack davies attack differential cryptanalysis harvest now decrypt later impossible differential cryptanalysis improbable differential cryptanalysis integral cryptanalysis linear cryptanalysis meet in the middle attack mod n cryptanalysis related key attack sandwich attack slide attack xsl attack asymmetric ciphers edit asymmetric cryptography or public key cryptography is cryptography that relies on using two mathematically related 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 40 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 41 in 1980 one could factor a difficult 50 digit number at an expense of 10 12 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 10 12 operations advances in computing technology also meant that the operations could be performed much faster moore s law 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 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 to be used citation needed 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 42 attacking cryptographic hash systems edit this section needs expansion you can help by adding missing information april 2012 birthday attack hash function security summary rainbow table length extension attack side channel attacks edit main article side channel attack this 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