Impossible-Differential Attacks on block-cipher based Hash and Compression Functions using 3D and Whirlpool

Abstract

In this paper, we analyse block-cipher-based hash functions, which means hash functions that use block ciphers as compression functions in a mode of operation, such as Davies-Meyer (DM), Matyas-Meyer-Oseas (MMO) and Miyaguchi-Preneel (MP), for instance. We use impossible differentials (ID) to distinguish the compression (or hash) function from an ideal primitive (a random oracle) by detecting a nonrandom behavior. We applied an ID analysis to an 8-round variant of the 3D block cipher used in MMO mode, as a compression function of a hypothetical hash function. This attack effectively improves upon the previously known distinguishing ID attacks on reduced-round 3D. We can also attack a hash function using 3D as compression function in DM mode. Finally, we attacked the compression function in Whirlpool with a 5-round W cipher in MP mode with 2100 time and 264 memory.