VSH, an Efficient and Provable Collision-Resistant Hash Function

Abstract. We introduce VSH, very smooth hash, a new S-bit hash function that is provably collision-resistant assuming the hardness of finding nontrivial modular square roots of very smooth numbers modulo an Sbit composite. By very smooth, we mean that the smoothness bound is some fixed polynomial function of S. We argue that finding collisions for VSH has the same asymptotic complexity as factoring using the Number Field Sieve factoring algorithm, i.e., subexponential in S. VSH is theoretically pleasing because it requires just a single multiplication modulo the S-bit composite per (S) message-bits (as opposed to O(log S) message-bits for previous provably secure hashes). It is relatively practical. A preliminary implementation on a 1GHz Pentium III processor that achieves collision resistance at least equivalent to the dif

• Type: Conference
• Year: 2006
• Where: EUROCRYPT
• Authors: Scott Contini, Arjen K. Lenstra, Ron Steinfeld
• Keywords: Cryptology, EUROCRYPT 2006, Nontrivial Modular Square, S-bit Hash Function, Smooth Hash