[Resource Topic] 2024/679: Isotropic Quadratic Forms, Diophantine Equations and Digital Signatures

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Title:
Isotropic Quadratic Forms, Diophantine Equations and Digital Signatures

Authors: Martin Feussner, Igor Semaev

Abstract:

This work introduces DEFI - 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.

ePrint: https://eprint.iacr.org/2024/679

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