Confirmation that some hash functions are not collision free

Abstract

Hash functions arc used to compress messages into digital signatures. A hash function has to be collision free; i.e., it must be computationally infeasible to construct different messages which out- put the same hash-value. This paper shows that five hash functions are not collision free, including the assumptions that an attacker can modify an initial value of the hash function. These hash functions are analyzed from the standpoints of their structure, the complementa- tion property and the weak keys of the block ciphers used in them. As a result, it is clear that many pairs of messages can be created to generate the same hash-values. Therefore, users desiring to use these hash functions should be notified of their weakness.