How to Construct Sufficient Condition in Searching Collisions of MD5

In Eurocrypt 2005, Wang et al. presented a collision attak on MD5. In their paper, they intoduced “Sufficient Condition” which would be needed to generate collisions. In this paper, we explain how to construct sufficent conditions of MD5 when a differential path is given. By applying our algorithm to a collision path given by Wang et al, we found that sufficient conditions introduced by them contained some unnecessary conditions. Generally speaking, when a differential path is given, corresponding sets of sufficient conditions is not unique. In our research, we analyzed the differential path found by Wang et al, and we found a different set of sufficient conditions from that of Wang et al. We have generated collisions by using our sifficient conditions.