Multi-collision resistance: a paradigm for keyless hash functions

Nir Bitansky, Yael Tauman Kalai, Omer Paneth
2018 Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2018  
We study the notion of multi-collision resistance of hash functions -a natural relaxation of collisionresistance that only guarantees the intractability of finding many (rather than two) inputs that map to the same image. An appealing feature of such hash functions is that unlike their collision-resistant counterparts, they do not necessarily require a key. Specifically, in the keyless setting, we only require that the size of collisions an adversarial algorithm can find is not much larger than
more » ... its description size, or non-uniform advice. We show how to replace collision resistance with multi-collision resistance in several foundational applications. Relying on such keyless functions, we improve on the best known round complexity for these applications. This includes: • 3-message zero-knowledge arguments for NP. • 3-message succinct arguments of knowledge for NP. • 4-message ε-zero-knowledge proofs for NP. • 5-message public-coin zero-knowledge arguments for NP. * MIT,
doi:10.1145/3188745.3188870 dblp:conf/stoc/BitanskyKP18 fatcat:wkozeczwgvhz7cmwj6ev4nmuki