Papers › Fast construction of irreducible polynomials over finite fields
Fast construction of irreducible polynomials over finite fields
Jean-Marc Couveignes, Reynald Lercier
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We present a randomized algorithm that on input a finite field K with q elements and a positive integer d outputs a degree d irreducible polynomial in K[x]. The running time is d^(1+ϵ(d)) ×(logq)^(5+ϵ(q)) elementary operations. The function ϵ in this expression is a real positive function belonging to the class o(1), especially, the complexity is quasi-linear in the degree d. Once given such an irreducible polynomial of degree d, we can compute random irreducible polynomials of degree d at the expense of d^(1+ϵ(d)) ×(logq)^(1+ϵ(q)) elementary operations only.
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