Paper 2026/2116 Original: eprint.iacr.org/2026/2116 ↗
Smooth evaluations of cyclotomic quadratics
Abstract
In this note we find large primes $p$ such that $\Phi_k(p)$ is $B$-smooth for the cyclotomic polynomials $\Phi_k$, with $k = 3,4$ and $6$, and a sufficiently small smoothness bound $B$. These primes hence provide the first instantiation of integer factoring challenges that, a priori would be difficult to factor but, are actually easy to factor with traditional algorithms not typically used in practice.
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2026-09-19: last updated
- 2026-09-19: published
- Short URL
- https://ia.cr/2026/2116
- License
- https://creativecommons.org/publicdomain/zero/1.0/
BibTeX
@misc{cryptoeprint:2026/2116,
author = {Bruno Sterner},
title = {Smooth evaluations of cyclotomic quadratics},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/2116},
year = {2026},
url = {https://eprint.iacr.org/2026/2116}
}