Diffusion Analysis of Message Expansion in STITCH-256

Cryptographic hash functions are built up from individual components, namely pre-processing, step transformation, and final processing. Some of the hash functions, such as SHA-256 and STITCH-256, employ non-linear message expansion in their pre-processing stage. However, STITCH-256 was claimed to produce high diffusion in its message expansion. In a cryptographic algorithm, high diffusion is desirable as it helps prevent an attacker finding collision-producing differences, which would allow one to find collisions of the whole function without resorting to a brute force search. In this paper, we analyzed the diffusion property of message expansion of STITCH-256 by observing the effect of a single bit difference over the output bits, and compare the result with that of SHA-256. We repeated the same procedure in 3 experiments of different round. The results from the experiments showed that the minimal weight in the message expansion of STITCH-256 is very much lower than that in the message expansion of SHA-256, i.e. message expansion of STITCH-256 produce high diffusion. Significantly, we showed that the probability to construct differential characteristic in the message expansion of STITCH-256 is reduced.