Paper 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.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint.
- Keywords
- Digital signaturesIsotropic quadratic formsDiophantine equations
- Contact author(s)
-
martin feussner @ uib no
igor semaev @ uib no - History
- 2024-11-05: revised
- 2024-05-03: received
- See all versions
- Short URL
- https://ia.cr/2024/679
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2024/679,
author = {Martin Feussner and Igor Semaev},
title = {Isotropic Quadratic Forms, Diophantine equations and Digital Signatures, {DEFIv2}},
howpublished = {Cryptology {ePrint} Archive, Paper 2024/679},
year = {2024},
url = {https://eprint.iacr.org/2024/679}
}