A study on the upper bounds of the maximum differential/linear characteristic probabilities of Feistel ciphers with SPN round function

摘要

This paper studies the upper bounds of the maximum differential/linear characteristic probabilities of Feistel ciphers with SPN round function. In the same way as SPN ciphers, we consider the minimum number of differentially/linearly active s-boxes, which are proportion to the upper bounds of these probabilities, in order to evaluate the security against differential/linear attacks. The purpose of this work is to clarify the minimum numbers of active s-boxes in some consecutive rounds of Feistel ciphers, i.e., in three, four, six, eight, and twelve consecutive rounds, using differential/linear branch numbers B{sub}d, B{sub}l. As a result, we clarified that the minimum number of differentially (resp. linearly) active s-boxes are 2, B{sub}d (B{sub}l), B{sub}d + 2 (B{sub}l + 2), 2B{sub}d + 1 (2B{sub}l + 1), and 3B{sub}d + 1 (3B{sub}l + 1), respectively.