Strict Avalanche Criterion of SHA-256 and Sub-Function-Removed Variants

Abstract

The measure of diffusion, the property of dissipating patterns and statistical structures in cryptographic transformations, serves as a valuable heuristic for assessing the obscurity of patterns that could lead to collisions. As with many cryptographic hash functions, SHA-256 is thought to exhibit the property of diffusion. While SHA-256’s diffuse output is loosely documented, even less is known about how the diffusion rate changes across the 64 rounds in its compression function and how the algorithm’s individual sub-functions contribute to the overall diffusion. The diffusion of the unmodified compression function is initially measured using the Strict Avalanche Criterion (SAC), with the aim of understanding the alteration in diffusion across the 64 rounds of compression. The level to which sub-functions affect diffusion is subsequently measured, enabling potential prioritization of these sub-functions in future collision attacks. To accomplish this, the compression function is modified by removing sub-functions, and the diffusion of these new variants is measured. While the SAC measurements of each function eventually plateau close to the 50% target, no function, including the unmodified compression function, strictly meets the SAC, and multiple variant functions diffuse at comparatively slower rates.