Polynomial evaluation over finite fields: new algorithms and complexity   bounds
  An efficient evaluation method is described for polynomials in finite fields. Its complexity is shown to be lower than that of standard techniques when the degree of the polynomial is large enough. Applications to the syndrome computation in the decoding of Reed-Solomon codes are highlighted. 
Michele Elia, Joachim Rosenthal, Davide Schipani
cs.IT math.IT math.NT