Paper 2026/2452 Original: eprint.iacr.org/2026/2452 ↗
Genericity in multivariate cryptography
Abstract
The results in this paper establish the genericity of some properties of the ideals and varieties generated by UOV public keys, in particular the equidimensionality of the UOV varieties and the radicality of public key ideals. These genericity results justify the various regularity assumptions that are made on polynomial systems of equations arising in the cryptanalysis of UOV and its variants. We also provide examples in the recent literature showing how genericity questions arise in crypt- analysis and why genericity should be taken into consideration when de- signing cryptographic schemes. Lastly, we perform a retrospective study of various cryptographic schemes through the viewangle of genericity. We identify several cases in which non-genericity led to the cryptanaly- sis of the scheme, but also provide a counter-example of a scheme whose non-genericity does not seem easy to exploit.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2026-10-12: last updated
- 2026-10-12: published
- Short URL
- https://ia.cr/2026/2452
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2026/2452,
author = {Simon Abelard and Pierre Pébereau and Mohab Safey El Din},
title = {Genericity in multivariate cryptography},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/2452},
year = {2026},
url = {https://eprint.iacr.org/2026/2452}
}