Faster integer and polynomial multiplication using cyclotomic coefficient rings

12/11/2017

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by   David Harvey, et al.

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We present an algorithm that computes the product of two n-bit integers in O(n log n (4√(2))^log^* n) bit operations. Previously, the best known bound was O(n log n 6^log^* n). We also prove that for a fixed prime p, polynomials in F_p[X] of degree n may be multiplied in O(n log n 4^log^* n) bit operations; the previous best bound was O(n log n 8^log^* n).