Paper 2024/679 Original: eprint.iacr.org/2024/679 ↗

Isotropic Quadratic Forms, Diophantine equations and Digital Signatures, DEFIv2

Abstract

This work introduces DEFIv2 - an efficient hash-and-sign digital signature scheme based on isotropic quadratic forms over a commutative ring of characteristic 0. The form is public, but the construction is a trapdoor that depends on the scheme's private key. For polynomial rings over integers and rings of integers of algebraic number fields, the cryptanalysis is reducible to solving a quadratic Diophantine equation over the ring or, equivalently, to solving a system of quadratic Diophantine equations over rational integers. It is still an open problem whether quantum computers will have any advantage in solving Diophantine problems.