## Cryptology ePrint Archive: Report 2017/990

Bounds on the Differential Branch Number of Permutations

Sumanta Sarkar and Habeeb Syed

Abstract: Nonlinear permutations (S-boxes) are key components in block ciphers. Differential branch number measures the diffusion power of a permutation. Differential branch number of nonlinear permutations of $\mathbb{F}_2^n$ has not been analyzed, although it is well studied for linear permutations. In this paper we obtain a bound on differential branch number of permutations (both linear and nonlinear) of $\mathbb{F}_2^n$. We also show that in case of $\mathbb{F}_2^4$, the maximum differential branch number can be achieved only by affine permutations.

Category / Keywords: secret-key cryptography / Permutation, S-box, differential branch number, block cipher, Griesmer bound