Multivariates Polynomials for Hashing

We propose the idea of building a secure hash using quadratic or higher degree multivariate polynomials over a finite field as the compression function. We analyze some security properties and potential feasibility, where the compression functions are randomly chosen highdegree polynomials, and show that under some plausible assumptions, high-degree polynomials as compression functions has good properties. Next, we propose to improve on the efficiency of the system by using some specially designed polynomials generated by a small number of random parameters, where the security of the system would then relies on stronger assumptions, and we give empirical evidence for the validity of using such polynomials.

• Type: Conference
• Year: 2007
• Where: CISC
• Authors: Jintai Ding, Bo-Yin Yang
• Keywords: CISC 2007, Compression Functions, Cryptology, Degree Multivariate Polynomials, Plausible Assumptions