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Unformatted text preview: carefully chosen, inputs to Sboxes can produce the same output [436]. It is possible to obtain the same output of a single DES round by changing bits in only three neighboring Sboxes [487]. Shamir noticed that the Sboxes entries appeared to be somewhat imbalanced, but wasn’t about to turn that imbalance into an attack [1423]. (He mentioned a feature of the fifth Sbox, but it took another eight years before linear cryptanalysis exploited that feature.) Other researchers showed that publicly known design principles could be used to generate Sboxes with the observed characteristics [266]. Additional Results
There were other attempts to cryptanalyze DES. One cryptographer looked at nonrandomness based on spectral tests [559]. Others analyzed sequences of linear factors, but their attack failed after eight rounds [1297,336,531]. A 1987 unpublished attack by Donald Davies exploited the way the expansion permutation repeats bits into adjacent Sboxes; this attack is also impractical after eight rounds [172,429]. 12.4 Differential and Linear Cryptanalysis Differential Cryptanalysis
In 1990, Eli Biham and Adi Shamir introduced differential cryptanalysis [167,168,171,172]. This is a new method of cryptanalysis, heretofore unknown to the public. Using this method, Biham and Shamir found a chosenplaintext attack against DES that was more efficient than brute force. Differential cryptanalysis looks specifically at ciphertext pairs: pairs of ciphertexts whose plaintexts have particular differences. It analyzes the evolution of these differences as the plaintexts propagate through the rounds of DES when they are encrypted with the same key. Simply, choose pairs of plaintexts with a fixed difference. The two plaintexts can be chosen at random, as long as they satisfy particular difference conditions; the cryptanalyst does not even have to know their values. (For DES, the term “difference” is defined using XOR. This can be different for different algorithms.) Then, using the differences in the resulting ciphertexts, assign different probabilities to different keys. As you analyze more...
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This note was uploaded on 10/18/2010 for the course MATH CS 301 taught by Professor Aliulger during the Fall '10 term at Koç University.
 Fall '10
 ALIULGER
 Cryptography

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