By Eli Biham

DES, the information Encryption ordinary, is the simplest recognized and most generally used civilian cryptosystem. It was once constructed via IBM and followed as a US nationwide usual within the mid 1970`s, and had resisted all assaults within the final 15 years. This e-book provides the 1st winning assault that could holiday the whole sixteen around DES speedier than through exhaustive seek. It describes in complete element, the radical means of Differential Cryptanalysis, and demonstrates its applicability to a wide selection of cryptosystems and hash capabilities, together with FEAL, Khafre, REDOC-II, LOKI, Lucifer, Snefru, N-Hash, and plenty of converted models of DES. The method used bargains beneficial insights to somebody drawn to info protection and cryptography, and issues out the intricacies of constructing, comparing, checking out, and enforcing such schemes. This e-book was once written through of the field`s best researchers, and describes state of the art study in a transparent and fully contained demeanour.

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**Extra resources for Differential Cryptanalysis of the Data Encryption Standard**

**Example text**

DES Reduced to Four Rounds 35 Given four encrypted pairs we use a separate counting procedure for each one of the seven S boxes in the fourth round. We try all the 64 possible values of SKd and check whether S(SEd E9 SKd) E9 S(SEd E9 SKd) = SOd· For each key we count the number of pairs for which the test succeeds. The right key value is suggested by all the pairs since we use a characteristic with probability 1, for which all the pairs are right pairs. The other 63 key values may occur in some of the pairs.

The method is as follows: 1. Choose an appropriate plaintext XOR. 2. Create an appropriate number of plaintext pairs with the chosen plaintext XOR, encrypt them and keep only the resultant ciphertext pairs. 3. For each pair derive the expected output XOR of as many S boxes in the last round as possible from the plaintext XOR and the ciphertext pair. (Note that the input pair of the last round is known since it appears as part of the ciphertext pair). 22 3. Introduction to Differential Cryptanalysis 4.

8 5 ) of the wrong pairs can be discarded a-priori. For DES reduced to ten or more rounds, the signal to noise ratio of the 3R-attacks becomes too small, and thus 3R-attacks on these variants are not recommended. 2 2R-ATTACKS In 2R-attacks counting can be done on all the bits of the subkey of the last round. Wrong pairs can be discarded if the input XORs of the S boxes in the previous round may not cause the expected output XORs. 8. In DES reduced to nine rounds the 48 bits of Kg can be found using 226 pairs using the seven-round characteristic.