Improved Collision Attack on MD4

In this paper, we propose an attack method to find collisions of MD4 hash function. This attack is the improved version of the attack which was invented by Xiaoyun Wang et al [1]. We were able to find collisions with probability almost 1, and the average complexity to find a collision is upper bounded by three times of MD4 hash operations. This result is improved compared to the original result of [1] where the probability were from 2−6 to 2−2, and the average complexity to find a collision was upper bounded by 2 MD4 hash operations. We also point out the lack of sufficient conditions and imprecise modifications for the original attack in [1]. keywords: Collision Attack, MD4, Hash Function, Message Modification