Paper 2026/2172
A New Prime-Norm Ideal Sampling for SQIsign
Abstract
SQIsign samples a random ideal of odd prime norm at every key generation and every signature through $\mathbf{PrimeNormIdealInertSampling}$. We revisit this step from a new perspective: the inert ideals of a given norm form a circle modulo the norm, and drawing lines through a fixed point of this circle turns a single random parameter into an ideal, hitting each ideal exactly once. Compared with the reference implementation, the new algorithm requires one modular inversion and a handful of additions and multiplications. It achieves $13.76\times$ speed-up at NIST security level I in SQIsign while producing an uniform output.
Metadata
- Available format(s)
-
PDF
- Category
- Implementation
- Publication info
- Preprint.
- Contact author(s)
- jcuyo613 @ gmail com
- History
- 2026-09-26: approved
- 2026-09-23: received
- See all versions
- Short URL
- https://ia.cr/2026/2172
- License
-
CC0
BibTeX
@misc{cryptoeprint:2026/2172,
author = {Li-Jie Jian},
title = {A New Prime-Norm Ideal Sampling for {SQIsign}},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/2172},
year = {2026},
url = {https://eprint.iacr.org/2026/2172}
}
