The sufficient conditions for keeping desired differential path of MD5 was discussed. By analyzing the expanding of subtraction difference, differential characters of Boolean functions, and the differential characters of shift rotation, the sufficient conditions for keeping desired differential path could be obtained. From the differential characters of shift rotation, the lacked sufficient conditions were found. Then an algorithm that reduces the number of trials for finding collisions were presented. By restricting search space, search operation can be reduced to 2 34 for the first block and 2 30 for the second block. The whole attack on the MD5 can be accomplished within 20 hours using a PC with 1.6 G CPU.
