### On Squaring Modulo Mersenne Numbers

##### Abstract

During the design of a new primitive inspired by Squash we accidentally stumbled on the observation described in this note. Let $n$ be a $k$-bit Mersenne number whose factors are unknown. Consider an $\ell$-bit secret number $x=2^{k/2}a+b$. We observe that there are parameter configurations where a chunk of the value $b^2$ is leaked even if $k<2\ell$. This observation does not endanger any known scheme and in particular not Squash.

Available format(s)
Category
Implementation
Publication info
Preprint.
Keywords
Squash Mersenne Squaring
Contact author(s)
david naccache @ ens fr
ofer friedman @ ens fr
History
2022-09-12: approved
See all versions
Short URL
https://ia.cr/2022/1197

CC0

BibTeX

@misc{cryptoeprint:2022/1197,
author = {David Naccache and Ofer Yifrach-Stav},
title = {On Squaring Modulo Mersenne Numbers},
howpublished = {Cryptology ePrint Archive, Paper 2022/1197},
year = {2022},
note = {\url{https://eprint.iacr.org/2022/1197}},
url = {https://eprint.iacr.org/2022/1197}
}

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