Finding small roots for bivariate polynomials over the ring of integers (Q6556570)

The paper under review deals with finding small roots for a bivariate equation. In 1996 Coppersmith proposed an algorithm to solve a single variable polynomial equation of degree \(k\) modulo an integer \(N\), provided a solution smaller than \(N^{1/k}\) exists. In this direction he also developed a method to solve integer polynomial equations in two variables. Later in 2011, \textit{H. Cohn} and \textit{N. Heninger} [Adv. Math. Commun. 9, No. 3, 311--339 (2015; Zbl 1355.65064)] proposed an ideal form of small root finding of an univariate polynomial equation over polynomial rings, number fields, and function fields. This paper extends these concepts to number fields, presenting a heuristic algorithm for finding small roots of bivariate polynomials modular ideals in number fields.