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New Method for Bounding the Maximum Differential Probability for SPNs and ARIA
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Block Cipher and Stream Cipher
New Method for Bounding the Maximum Differential Probability for SPNs and ARIA Hong-Su Cho1  , Soo Hak Sung2 , Daesung Kwon3 , Jung-Keun Lee3 , Jung Hwan Song4 and Jongin Lim1
| (1) |
Graduate School of Information Security, Korea University, 1, 5-Ka, Anam-dong, Sungbuk-ku, Seoul 136-701, Korea |
| (2) |
Department of Computing information & mathematics, Paichai University, 426-6 Doma-dong, Seo-gu, Daejeon 302-735, Korea |
| (3) |
National Security Research Institute, 161 Gajeong-dong, Yuseong-gu, Daejeon 305-350, Korea |
| (4) |
Department of Mathematics, Hanyang University, 17 Haengdang-dong, Seongdong-gu, Seoul 133-791, Korea |
Abstract
By considering the number of independent variables, we present a new method for finding an upper bound on the maximum differential probability (MDP) for r( r  2)-round substitution-permutation networks (SPNs). It first finds an upper bound for 2-round SPNs and then uses a recursive technique for r( r 3)-round SPNs. Our result extends and sharpens known results in that it is more effective for calculating MDP for r( r 3)-round SPNs and applicable to all SPNs. By applying our method to ARIA, we get an estimated bound of 1.5 × 2 –98 on MDP for 6-round ARIA.
Keywords: Cryptography, Differential cryptanalysis, Linear cryptanalysis, Substitution-permutation networks, Branch number, Independent variables, AES, ARIA.
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