Theory of Cryptography

Volume 3378 of the series Lecture Notes in Computer Science pp 445-456

Sufficient Conditions for Collision-Resistant Hashing

  • Yuval IshaiAffiliated withComputer Science Department, Technion
  • , Eyal KushilevitzAffiliated withComputer Science Department, Technion
  • , Rafail OstrovskyAffiliated withComputer Science Department, UCLA


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.


Collision-resistant hash functions homomorphic encryption private information-retrieval