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**2022/1273**

**Title:**

A Conjecture From a Failed Cryptanalysis

**Authors:**
David Naccache, Ofer Yifrach-Stav

**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.

**ePrint:**
https://eprint.iacr.org/2022/1273

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