### A Conjecture From a Failed Cryptanalysis

##### Abstract

This note describes an observation discovered during a failed cryptanalysis attempt. Let $P(x,y)$ be a bivariate polynomial with coefficients in $\mathbb{C}$. Form the $n\times n$ matrices $L(n)$ whose elements are defined by $P(i,j)$. Define the matrices $M(n)=L(n)-\mbox{ID}_n$. It appears that $\mu(n)=(-1)^n\det(M_n)$ is a polynomial in $n$ that we did not characterize. We provide a numerical example.

Available format(s)
Category
Attacks and cryptanalysis
Publication info
Preprint.
Keywords
Conjecture Matrices Polynomials
Contact author(s)
david naccache @ ens fr
ofer friedman @ ens fr
History
2022-09-27: last of 2 revisions
See all versions
Short URL
https://ia.cr/2022/1273

CC0

BibTeX

@misc{cryptoeprint:2022/1273,
author = {David Naccache and Ofer Yifrach-Stav},
title = {A Conjecture From a Failed Cryptanalysis},
howpublished = {Cryptology ePrint Archive, Paper 2022/1273},
year = {2022},
note = {\url{https://eprint.iacr.org/2022/1273}},
url = {https://eprint.iacr.org/2022/1273}
}

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