Finding good differential patterns for attacks on SHA-1

In this paper we analyse properties of the message expansion algorithm of SHA-1 and describe a method of finding differential patterns that may be used to attack reduced versions of SHA-1. We show that the problem of finding optimal differential patterns for SHA-1 is equivalent to the problem of finding minimal weight codeword in a large linear code. Finally, we present a number of patterns of different lengths suitable for finding collisions and near-collisions and discuss some bounds on minimal weights of them.