Paper 2024/763

Class-Average Differential Uniformity and Fixed-Instance Constraints in Modular and Rounded Feistel Components

Abstract

This paper analyzes differential probabilities in one Feistel round with binary-encoded modular-linear maps or rounded linear maps as internal components. For any fixed round key and any nonzero input difference chosen independently of the matrix instance, the output-difference distribution is uniform after averaging over the instance distribution. For a fixed instance, the 2-adic valuations of the relevant matrix entries deterministically fix certain output-difference bits. We consider an adversary that selects a low-weight input difference maximizing the number of fixed bits and derive lower bounds on the restricted maximum differential probability and its average over instances. The matrix-averaged lower bound is expressed in terms of the exponential moment of the maximum fixed-bit count and is compared with the generic lower bound induced by differential-pair symmetry.