Computing Frobenius maps and factoring polynomials

Authors:
Joachim von zur Gathen;Victor Shoup
Affiliations:
Department of Computer Science, University of Toronto, Toronto, Ontario M5S 1A4, Canada;Department of Computer Science, University of Toronto, Toronto, Ontario M5S 1A4, Canada
Venue:
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Year:
1992

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Abstract

A new probabilistic algorithm for factoring univariate polynomials over finite fields is presented whose asymptotic running time improves upon previous results. To factor a polynomial of degree n over Fq, the algorithm uses O((n2 + n log q)•(log n)2 log log n) arithmetic operations in Fq. The main technical innovation is a new way to compute Frobenius and trace maps in the ring of polynomials modulo the polynomial to be factored.