Paper 2022/184

Exploring SAT for Cryptanalysis: (Quantum) Collision Attacks against 6-Round SHA-3 (Full Version)

Abstract

In this work, we focus on collision attacks against instances of SHA-3 hash family in both classical and quantum settings. Since the 5-round collision attacks on SHA3-256 and other variants proposed by Guo et al. at JoC~2020, no other essential progress has been published. With a thorough investigation, we identify that the challenges of extending such collision attacks on SHA-3 to more rounds lie in the inefficiency of differential trail search. To overcome this obstacle, we develop a SAT-based automatic search toolkit. The tool is used in multiple intermediate steps of the collision attacks and exhibits surprisingly high efficiency in differential trail search and other optimization problems encountered in the process. As a result, we present the first 6-round classical collision attack on SHAKE-128 with time complexity $2^{123.5}$, which also forms a quantum collision attack with quantum time ${{2^{67.25}}/{\sqrt{S}}}$, and the first 6-round quantum collision attack on SHA3-224 and SHA3-256 with quantum time ${{2^{97.75}}/{\sqrt{S}}}$ and ${{2^{104.25}}/{\sqrt{S}}}$, both with negligible requirement of classical and quantum memory. The fact that classical collision attacks do not apply to 6-round SHA3-224 and SHA3-256 shows the higher coverage of quantum collision attacks, which is consistent with that on SHA-2 observed by Hosoyamada and Sasaki at CRYPTO~2021.