A Conjecture From a Failed Cryptanalysis

David Naccache; Ofer Yifrach-Stav

Paper 2022/1273

A Conjecture From a Failed Cryptanalysis

David Naccache, École Normale Supérieure - PSL

Ofer Yifrach-Stav, École Normale Supérieure - PSL

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.

Metadata

Available format(s): PDF
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; 2022-09-26: received; See all versions
Short URL: https://ia.cr/2022/1273
License: 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},
      url = {https://eprint.iacr.org/2022/1273}
}