Randomized root finding over finite fields using tangent Graeffe transforms
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Abstract

Consider a finite field whose multiplicative group has smooth cardinality. We study the problem of computing all roots of a polynomial that splits over , which was one of the bottlenecks for fast sparse interpolation in practice. We revisit and slightly improve existing algorithms and then present new randomized ones based on the Graeffe transform. We report on our implementation in the Mathemagix computer algebra system, confirming that our ideas gain by an order of magnitude in practice.

Authors: Bruno Grenet, Joris van der Hoeven, Grégoire Lecerf

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