Abstract: Hash functions arc widely used in business, military field etc. Therefore, the attack to Hash functions has important meaning in theory and in practical application. Since professor Wang proposed differential attack algorithm and succeeded to break SHA 1, MD5 , RIPEMD，MD4，this algorithm has been paid more and more attention. However, Pro Wang do not supply the method to get difference and differential path. Experts at home and abroad guessed that she made it by hand with her outstanding intuition. Therefore,finding the method to get difference and differential path becomes hotspot. We must tackle the circle shift difference and select the high probability sufficient conditions when constructing the differential path. This paper verified there arc four conditions and gave their probability and compared them with each other.

Key words: MD5，Hash functions, Differential attack, Tunncl technique, Multi-message modification method