Yet Another Definition of Weak Collision Resistance and Its Analysis
In this article, a new definition of weak collision resistance is presented following the definition of weak one-wayness. Collision resistance is a security notion of cryptographic hash functions. A collision of a hash function is a pair of different inputs which give the same output. In the new definition, weak collision resistance means that the probability of failing to find a collision is not negligible. This weak collision resistance is then analyzed. First, it is shown that there really exist weakly collision resistant hash functions if collision resistant ones exist. Second, it is shown that weak collision resistance can be amplifiable, that is, (strongly) collision resistant hash functions are constructed from a certain kind of weakly collision resistant ones. An example of weakly collision resistant hash functions is also presented to which the proposed amplification method is applicable.
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