RECOVERING ZEROS OF POLYNOMIALS MODULO A PRIME

Let p be a prime and F-p the finite field with p elements. We show how, when given an irreducible bivariate polynomial F is an element of F-p[X, Y] and an approximation to a zero, one can recover the root efficiently, if the approximation is good enough. The strategy can be generalized to polynomials in the variables X-1,..., X-m over the field F-p. These results have been motivated by the predictability problem for nonlinear pseudorandom number generators and other potential applications to cryptography.