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I have a bivariate modular polynomial of shape $$f(x,y)=x^2y-g(x)\equiv 0\bmod q$$ where $q=(2p-1)(2p+1)$ is a product of two primes $2p-1$ and $2p+1$, $g(x)\in\mathbb Z[x]$ is of degree four and $f(...

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 $f$, ...

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 $\...

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,...

I wonder how well arbitrary Diophantine equations can be used to make one time digital signature schemes. For our one-time digital signature scheme, the public key is a collection of polynomials $f_1(...

The paper Polynomial-Time Quantum Algorithms for Pell's Equation and the Principal Ideal Problem claims There are reductions from factoring to solving Pell’s equation, and from solving Pell’s ...