Some computational aspects of root finding in GF(qm)
This paper is an implementation report comparing several variations of a deterministic algorithm for finding roots of polynomials in finite extension fields. Running times for problem instances in fields GF(2m), including m>1000, are given. Comparisons are made between the variations, and improvements achieved in running times are discussed.
Unable to display preview. Download preview PDF.
- [Berl68]E.R. Berlekamp, Algebraic Coding Theory, McGraw-Hill, New York, 1968.Google Scholar
- [Berl70]E.R. Berlekamp, “Factoring polynomials over large finite fields”, Math. Comp. 24 (1970), 713–735.Google Scholar
- [CaZa81]D.G. Cantor and H. Zassenhaus, “A new algorithm for factoring polynomials over finite fields”, Math. Comp. 36 (1981), 587–592.Google Scholar
- [Lidl83]R. Lidl and H. Niederreiter, Finite Fields, Addison-Wesley, 1983.Google Scholar
- [Mull88]R.C. Mullin, I.M. Onyszchuk, S.A. Vanstone and R.M. Wilson, “Optimal normal bases in GF(p n)”, Discrete Applied Math. (to appear).Google Scholar
- [Rabi80]M.O. Rabin, “Probabilistic algorithms in finite fields”, SIAM J.Comput. 9 (1980), 273–280.Google Scholar
- [vaVa88]P.C. van Oorschot and S.A. Vanstone, “A geometric approach to root finding in GF(q m)”, IEEE Transactions on Information Theory (to appear).Google Scholar