Abstract
We consider the problem of factoring polynomials overGF(p) for those prime numbersp for which all prime factors ofp− 1 are small. We show that if we have a primitivet-th root of unity for every primet dividingp− 1 then factoring polynomials overGF(p) can be done in deterministic polynomial time.
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References
L.Adleman, G.Miller and K.Manders, On taking roots in finite fields;Proc. 18th IEEE Symp. on Foundations of Computer Science, (1977), 175–178.
E. R.Berlekamp,Algebraic coding theory; McGraw-Hill, 1968.
E. R. Berlekamp, Factoring polynomials over large finite fields;Math. Computation,24 (1970), 713–735.
J. von zur Gathen, Factoring polynomials and primitive elements for special primes;Theoretical Computer Science,52 (1987), 77–89.
M. A.Huang, Riemann Hypothesis and finding roots over finite fields;Proc. 17th ACM Symp. on Theory of Computing, (1985), 121–130.
D. E.Knuth,The art of computer programming; Vol. 2, Seminumerical algorithms Addison-Wesley Publishing Co., 1981.
R.Lidl and H.Niederreiter,Finite fields; Addison-Wesley Publishing Co., 1983.
R. T. Moenck, On the efficiency of algorithms for polynomial factoring;Mathematics of Computation,31 (1977), 235–250.
L.Rónyai, Factoring polynomials over finite fields;Proc. 28th IEEE Symp. on Foundations of Computer Science, (1987), 132–137.
R. J. Schoof, Elliptic curves over finite fields and the computation of square roots modp;Mathematics of Computation,44 (1985), 483–494.
D. Shanks, Five number-theoretic algorithms; inProc. 1972 Number Theory Conference, University of Colorado, Boulder, 1972, 217–224.
A.Tonelli,Göttinger Nachrichten, (1891), 344–346. Also in L. E.Dickson,History of the theory of numbers, Chelsea, New York, Vol. I, 215.
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Research partially supported by Hungarian National Foundation for Scientific Research, Grant 1812.