Matrix representation of conditions for the collision attack of SHA-1 and its application to the message modification

Abstract

In this paper, we propose a matrix representation of Chaining Variable Condition (CVC) and Message Condition (MC) for the collision attack on the hash function SHA-1. Then we apply this to an algorithm for constructing the Message Modification procedure in order to reduce the complexity for the collision attack of SHA-1. Message Modification is one of the most important techniques to search for a collision of SHA-1. Our approach will clarify how to effectively construct a "good" message modification procedure. By using our algorithm, we calculate some experiments of Message Modification for attacking SHA-1 based on the Disturbance Vector and the Differential Path presented by Wang et al. Then we show the results of constructing some Message Modifications applicable to CVC up to step 26. © 2010 Springer-Verlag.