Construction of Nonlinear Optimal Diffusion Functions over Finite Fields

Abstract

The diffusion function with large branch number is a fundamental building block in the construction of many block ciphers to achieve provable bounds against differential and linear cryptanalysis. Conventional diffusion functions, which are constructed based on linear error-correction code, has the undesirable side effect that a linear diffusion function by itself is “transparent” (i.e., has transition probability of 1) to differential and linear cryptanalysis. Nonlinear diffusion functions are less studied in cryptographic literature, up to now. In this paper, we propose a practical criterion for nonlinear optimal diffusion functions. Using this criterion we construct generally a class of nonlinear optimal diffusion functions over finite field. Unlike the previous constructions, our functions are non-linear, and thus they can provide enhanced protection against differential and linear cryptanalysis.