Study the function of building blocks in SHA Family

TL;DR

This paper analyzes the roles of specific components in SHA-256, demonstrating the importance of certain functions for security and exploring message expansion properties through experimental analysis.

Contribution

It shows the applicability of disturbance correction strategies to SHA-256 and proves the critical security role of the functions Σ and σ.

Findings

Functions Σ and σ are essential for SHA-256 security.

Variants without these functions can be broken with 2^64 hash operations.

Existence of low-weight expanded messages in XOR-linearised variants.

Abstract

In this paper we analyse the role of some of the building blocks in SHA-256. We show that the disturbance correction strategy is applicable to the SHA-256 architecture and we prove that functions $\Sigma$, $\sigma$ are vital for the security of SHA-256 by showing that for a variant without them it is possible to find collisions with complexity 2 64 hash operations. As a step towards an analysis of the full function, we present the results of our experiments on Hamming weights of expanded messages for different variants of the message expansion and show that there exist low-weight expanded messages for XOR-linearised variants.