Taking pth Roots Modulo Polynomials over Finite Fields

In this contribution we show how to find y(x) in the polynomial equation y(x) ^p t(x) mod f(x), where t(x), y(x) and f(x) are polynomials over the field GF(p ^m). The solution of such equations are thought for in many cases, e.g., for p = 2 it is a step in the so-called Patterson Algorithm for decoding binary Goppa codes.