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Related to this question Complexity of finding solutions of trapdoored polynomial. I am trying to build signature scheme based on hardness of finding points on varieties. Let $K$ be field and $M=K[x_1,...

Related to this question Cryptography signature scheme based on hardness of finding points on varieties. Working over $K=\mathbb{Q}[x_1,...,x_n,y_1,...y_m]$. By abuse of notation, for polynomial $f$, ...

The Schoof-Elkies-Atkin (SEA) algorithm (for counting points on elliptic curves over a finite field) performs computations over polynomials modulo some modular polynomials. Originally the "classical" ...

Added Wed 13 Apr 2022 I have written a short note with experimental data, which shows not all pseudo keys are good keys. Public key cryptography based on non-invertible matrices We got public key ...

One knows that (ordinary) Jacobians of hyperelliptic curves over a finite field $\mathbb F_q$ (mostly of genus 1 (elliptic curves) and 2) are extensively studied by cryptographers, as a platform for ...

This is related to cryptography and this question and another question. In short, we are asking about decomposing multivariate polynomial as sum of perfect powers of linear polynomials. Working over $\...