Abstract

. We present a new algorithm for finding an irreducible polynomial of specified degree over a finite field. Our algorithm is deterministic, and it runs in polynomial time for fields of small characteristic. We in fact prove the stronger result that the problem of finding irreducible polynomials of specified degree over a finite field is deterministic polynomial time reducible to the problem of factoring polynomials over the prime field. 1980 Mathematics Subject Classification (1985 revision). Primary 11T06. This research was supported by National Science Foundation grants DCR-8504485 and DCR-8552596. Appeared in Mathematics of Computation 54, pp. 435--447, 1990. A preliminary version of this paper appeared in Proceedings of the 29th Annual Symposium on Foundations of Computer Science, October 1988. 1. Introduction In this paper we present some new algorithms for finding irreducible polynomials over finite fields. Such polynomials are used to implement arithmetic in extension fields ...

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