Taking pth Roots Modulo Polynomials over Finite Fields

  • Authors:

  • Klaus Huber

  • Affiliations:

  • ES 21a, Deutsche Telekom AG, T-Systems Nova GmbH, 64276 Darmstadt, Germany

  • Venue:
  • Designs, Codes and Cryptography
  • Year:
  • 2003

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Abstract

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(pm). 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.