Abstract. We give a deterministic polynomial-time algorithm that computes a nontrivial rational point on an elliptic curve over a finite field, given a Weierstrass equation for the...
We study the polynomial reconstruction problem for low-degree multivariate polynomials over finite field F[2]. In this problem, we are given a set of points x ∈ {0, 1}n and ta...
Abstract. This paper shows that there is a close relationship between the Euclidean algorithm for polynomials and the Lanczos method for solving sparse linear systems, especially w...
Let Fq be the finite field of q elements, where q = ph. Let f(x) be a polynomial over Fq in n variables with m non-zero terms. Let N(f) denote the number of solutions of f(x) = 0 ...
In this paper we study the problem of explicitly constructing a dimension expander raised by [BISW04]: Let Fn be the n dimensional linear space over the field F. Find a small (ide...