[Resource Topic] 2017/1175: Short Solutions to Nonlinear Systems of Equations

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Short Solutions to Nonlinear Systems of Equations

Authors: Alan Szepieniec, Bart Preneel


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.

ePrint: https://eprint.iacr.org/2017/1175

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