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Jul 10 13:17 [raw]

From: colin@nyx10.cs.du.edu (Colin Plumb) Subject: Cryptanalysis of the GOST 28147-89 cipher The publication of this standard by Aleksandr Malchik and Whitfield Diffie of Sun, and Josef Pieprzyk and Leonid Tombak of the University of Wollongong seems to have attracted little attention. A few people have suggested that with a 256-bit key and 32 rounds, it is a good candidate replacement for the DES. I am not a skilled cryptanalyst, but my examination suggests that this is not a good idea. I'd like to share it and attract comments. Description of the cipher: The GOST cipher is very similar to the DES, except that - There are no initial and final permutations - There are 32 rounds - There is no 32->48 bit expansion - The subkey for each round is added, mod 2^32, to the data instead of XORed - The S-boxes are 4->4 bits - The S boxes are not defined by the standard - The permutation is a rotation 11 bits to the left (i.e. in the direction of the carries in the above addition) instead of DES's more complex permutation - The key schedule is taken from 8 32-bit words, which are used in the order 0-7,0-7,0-7,7-0 during encryption and 0-7,7-0,7-0,7-0 during decryption The 512 bits of S-box is considered a parameter of the cryptosystem that is developed using the standard, so I assume that given their use for a long period of time at many sites, they are not secret. Eli Biham and Adi Shamir's consideration of DES variants in their book Differential Analysis of the Data Encryption Standard is very useful here. Section 4.5.1 considers eliminating the permutation, which significantly weakens the cipher by dramatically reducing the avalanche effect. Section 4.5.3.1 considers replacing XOR by addition, which weakens the DES, but to me it seems reasonable to attribute that to throwing off the scrupulous optimisation of the S-boxes, and re-evaluating the S boxes should produce a cipher as strong. And section 4.5.6 considers eliminating the expansion, which also has a dramatic effect on the strength of the DES. The care with which the S-boxes were chosen is made particularly in sections 4.5.2, 4.5.4 and 4.5.5, but is also apparent throughout the book. Just this fact, that the GOST standard does not supply strong S-boxes, means that considerable work must be done to produce some. The combination of these simplifications makes me doubt that even doubling the number of rounds is sufficient to make this cipher match the strength of the DES. However, it is the simplification of the permutation, leading to a change in one input bit one round affecting one S-box which then affects two in the next round, three the round after that, and so on, taking eight rounds to full avalanche, that worries me most. I am not sure there is sufficient avalanching to provide strong security. Certainly much higher-probability differentials should be possible than with the DES. One possibility is that by choosing keys with a large number of 1 bits, carry propagation can produce avalanching between non-adjacent S-boxes. This reduces the effective key space from 256 bits, but this key space is considerably larger than necessary for security in any case, and almost certainly exceeds the strength of the cipher against analytic attack. Thus, it does not weaken the cipher against brute-force attack, while possibly increasing its strength against analytic attack. If this were not publicised, it raises the possibility that good keys are sparse, and someone not familair with the need would almost inevitably choose a weak one. Shades of the COMSEC endorsement program! Perhaps secret organizations have a great deal in common around the world. Admittedly that is wild speculation on my part, but it does seem quite attractive. That, and the lack of supplied good S-boxes, would mean that the standard would be almost useless in the hands of someone not already cryptographically savvy. But for these problems, I would strongly advise against adopting the cipher until these concerns have been analyzed more thoroughly. Any comments? Addendum: Instead of output feedback mode, the feedback-free stream mode advised by the GOST standaed is a variant of the counter mode that has been suggested for DES. The way it is done may be worthy of attention. The IV is first encrypted with the key. Then, for each block of random output, the two magic constants 0x01010101 and 0x01010104 are added, modulo 2^32-1 (in such a way that 0xffffffff is the preferred form of 0) to the two halves of the IV, which is then encrypted to produce the output. -- -Colin

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