Abstract
Several methods of computing irreducible polynomials over finite fields are presented. If preprocessing, depending only on p , is allowed for free, then an irreducible polynomial of degree at least n over Z p can be computed deterministically with O(n logp), i.e. O(output size), bit operations. The estimates for the preprocessing time depend on unproven conjectures.
Extended Abstract
Part of this work was done while the author was visiting Universität Zürich, and supported by Schweizerischer Nationalfonds, grant 2175-0.83, and by NSERC, grant 3-650-126-40. A complete version is available as Tech. Rep. 188/86, Department of Computer Science, University of Toronto.
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von zur Gathen, J. (1986). Irreducible polynomials over finite fields. In: Nori, K.V. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1986. Lecture Notes in Computer Science, vol 241. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-17179-7_15
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DOI: https://doi.org/10.1007/3-540-17179-7_15
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