A Matching Lower Bound on the Minimum Weight of SHA-1 Expansion Code

Recently, Wang, Yin, and Yu ([WYY05b]) have used a low weight codeword in the SHA-1 message expansion to show a better than brute force method to find collisions in SHA-1. The smallest minimum weight codeword they report has a (bit) weight of 25 in the last 60 of the 80 expanded words. In this paper we show, using a computer assisted method, that this is indeed the smallest weight codeword. In particular, we show that the minimum weight over F2 of any non-zero codeword in the SHA-1 (linear) message expansion code, projected on the last 60 words, is at least 25.