Cryptology ePrint Archive: Report 2017/1175

Short Solutions to Nonlinear Systems of Equations

Alan Szepieniec and Bart Preneel

Abstract: This paper presents a new hard problem for use in cryptography, called Short Solutions to Nonlinear Equations (SSNE). This problem generalizes the Multivariate Quadratic (MQ) problem by requiring the solution be short; as well as the Short Integer Solutions (SIS) problem by requiring the underlying system of equations be nonlinear. The joint requirement causes common solving strategies such as lattice reduction or Gröbner basis algorithms to fail, and as a result SSNE admits shorter representations of equally hard problems. We show that SSNE can be used as the basis for a provably secure hash function. Despite failing to find public key cryptosystems relying on SSNE, we remain hopeful about that possibility.

Category / Keywords: signature scheme, hard problem, post-quantum, MQ, SIS, SSNE, hash function

Original Publication (in the same form): Number Theory Methods in Cryptology - NuTMiC 2017

Date: received 1 Dec 2017

Contact author: alan szepieniec at esat kuleuven be

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Version: 20171206:030145 (All versions of this report)

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