Finding Collisions for a 45-Step Simplified HAS-V

Recent attacks on hash functions start by constructing a differential characteristic. By finding message pairs that satisfy this characteristic, a collision can be found. This paper describes the method of De Cannière and Rechberger to construct generalized characteristics for SHA-1 in more detail. This method is further generalized and applied to a simplified variant of the HAS-V hash function. Using these techniques, a characteristic for 45 steps is found, requiring an effort of about 2 compression function evaluations to find a colliding message pair. A lot of the message bits can still be freely chosen when using this characteristic, greatly increasing its usefulness.