Sufficient Conditions for Collision-Resistant Hashing

We present several new constructions of collision-resistant hash-functions (CRHFs) from general assumptions. We start with a simple construction of CRHF from any homomorphic encryption. Then, we strengthen this result by presenting constructions of CRHF from two other primitives that are implied by homomorphic-encryption: one-round private information retrieval (PIR) protocols and homomorphic one-way commitments.

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