Relation Between Successfulness of Birthday Attack on Digital Signature and Hash Function Irregularity

In many network communications it is crucial to be able to authenticate both the contents and the origin of a message. Digital signatures based on public key schemas are used for such authentication. In order to provide message authentication the signature must depend on the contents of the message being signed. Since the public key-based signature schemes take too much time to compute, hash functions that map messages to short digests h(M) are used. Among other desirable properties of hash functions, an interesting one is that it should be collision-resistant, that is it should be difficult to find two messages with the same hash value.

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