Faster polynomial multiplication over finite fields
Abstract
Let p be a prime, and let Mp(n) denote the bit complexity of multiplying two polynomials in Fp[X] of degree less than n. For n large compared to p, we establish the bound Mp(n) = O(n log n 8(log* n) log p), where log* is the iterated logarithm. This is the first known F\"urer-type complexity bound for Fp[X], and improves on the previously best known bound Mp(n) = O(n log n log log n log p).
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