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The related key attack on the full GOST block cipher with four or two related keys Marina Pudovkina National Nuclear Research University (Moscow Engineering-Physics Institute)

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The GOST block cipher ●Gosudarstvennyi standard Cryptographic Protection for Data Processing Systems, 1989 ●64-bit block cipher ● 32-round Feistel cipher

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The GOST block cipher ● The S-boxes are not specified in the standard, only that they are somehow supplied. All eight S-boxes are different; these are considered additional key material. ● The 256-bit secret key K is divided to eight 32-bit blocks: K 1, K 2,…, K 8. ● The key schedule produces round keys k 1, k 2,…,k 32 as follows:

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Related key attacks on GOST ● [FGHL09] Fleischmann E., Gorski M,, Huehne J.-H., Lucks S., Key recovery attack on full GOST block cipher with zero time and memory. Western European Workshop on Research in Cryptology 2009 ● The attack uses a related-key boomerang distinguisher technique ● The attack not allow to recover the secret key of the GOST block cipher with complexity less than the complexity of the exhaustive search

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Related key attacks on GOST ● [Rud10] Rudskoy V., On zero practical significance of “Key recovery attack on full GOST block cipher with zero time and memory”, ● The main idea from [FGHL09] ● Related-key boomerang distinguisher technique ● 18 related keys to recover the 256-bit secret key ● Work for random S-boxes [Rud10] (?) We get ● The attack works if = (1,0,0,0) is not a liner translator of S 1, i.e. for all {0,1} 4 we have where α U {0,1} 4

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Our attack with 4 related keys ● Step I. Finding the round key k 32 (= k 1 ) of the last round 1.The related-key boomerang distinguisher from [Rud10] 2. 4 related keys K, K, K , K ● Step II. Finding round keys k 31, k 30,…, k The related-key truncated differential distinguisher based on the distinguisher used in [KHLLK04] Ko Y., Hong S., Lee W., Lee S., Kang J.-S., Related key differential attacks on 27 rounds of xtea and full- round gost. FSE, v. 3017, Springer, Two related keys K, K

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Our attack with 4 related keys ● Step III. Finding round keys k 25, k 26 1.Combination related-key truncated differential and boomerang distinguishers 2.Two related keys K, K ● There are S-boxes for which the attack does not work ● The complexity depends on S-boxes ● To break GOST with S-boxes described in “Applied Cryptography” by B. Schneier we need 4 related keys, the probability of success is 0.92

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Our attack with 2 related keys ● Step I. Finding round keys k 32, k 31,…, k 27. The related- key truncated differential distinguisher based on the distinguisher used in [KHLLK04] ● Step II. Finding round keys k 25, k 26. Combination related-key truncated differential and boomerang distinguishers ● There are S-boxes for which the attack does not work ● The complexity depends on S-boxes ● We cannot break GOST using two related keys with S-boxes described in “Applied Cryptography” by B. Schneier

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Thank you for your attention!

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