On Building Hash Functions from Multivariate Quadratic Equations

Recent advances in hash functions cryptanalysis provide a strong impetus to explore new designs. This paper describes a new hash function mq-hash that depends for its security on the difficulty of solving randomly drawn systems of multivariate equations over a finite field. While provably achieving pre-image resistance for a hash function based on multivariate equations is relatively easy, na¨ıve constructions using multivariate equations are susceptible to collision attacks. In this paper, therefore, we describe a mechanism—also using multivariate quadratic polynomials—yielding the collision-free property we seek while retaining provable pre-image resistance. Therefore, mq-hash offers an intriguing companion proposal to the provably collision-free hash function vsh.

• Type: Conference
• Year: 2007
• Where: ACISP
• Authors: Olivier Billet, Matthew J. B. Robshaw, Thomas Peyrin
• Keywords: ACISP 2007, Hash Function, Hash Function Mq-hash, Multivariate Equations, Security Privacy