Boomerang and Slide-Rotational Analysis of the SM3 Hash Function

SM3 is a hash function, designed by Xiaoyun Wang et al. and published by the Chinese Commercial Cryptography Administration Office for the use of electronic authentication service system. The design of SM3 builds upon the design of the SHA-2 hash function, but introduces additional strengthening features. In this paper, we present boomerang distinguishers for the SM3 compression function reduced to 32 steps out of 64 steps with complexity 214.4, 33 steps with complexity 232.4, 34 steps with complexity 253.1 and 35 steps with complexity 2117.1. Examples of zero-sum quartets for the 32-step and 33-step SM3 compression function are provided. We also point out a slide-rotational property of SM3-XOR, which exists due to the fact that constants used in the steps are not independent.