Large ciphers - the random permutation. comparison of indicators statistical security block symmetric ciphers before the ukrainian competition

Abstract

This paper represents additional materials to prove the hypothesis that modern ciphers are asymptotically random substitutions. Here we compare statistics between real modern ciphers and their reduced models. The following indicators are considered: to be avalanche effect, completeness, degree of avalanche effect and degree of the strict avalanche criterion. We describe methods for determining these indicators and analyze the results of applying them to Ukrainian block cipher competitors and also for Rijndael and GOST ciphers. The presented results clearly confirm that the reduced models have practically the same statistics as their cipher prototypes discussed in this paper (Rijndael, GOST and Ukrainian block cipher competitors – Muhomor, Kalina, ADE, Labirint). This means we can build reduced models with randomness indicators that correspond to their big counterparts, and, therefore, the conclusions we get for 'small' ciphers can be applied to the real ciphers. In particular, it refers to the conclusion that both 'small' and real ciphers asymptotically acquire properties of random permutations. Correlative indicators in dynamics of their changes are generally the same as the results obtained from studying differential and linear properties for 'small' and real ciphers. We get additional evidence and arguments in favor of proposed method for measuring block ciphers security by studying their reduced models. As the additional result of the research, it was concluded that three of the four Ukrainian block cipher competitors have better statistic indicators than well-known Rijndael and thus are superior.