Welcome to the resource topic for 2022/1197
Title:
On Squaring Modulo Mersenne Numbers
Authors: David Naccache, Ofer Yifrach-Stav
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.
ePrint: https://eprint.iacr.org/2022/1197
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