Toward an Optimal Quantum Algorithm for Polynomial Factorization over Finite Fields

07/25/2018

∙

by   Javad Doliskani, et al.

∙

0

∙

share

We present a randomized quantum algorithm for polynomial factorization over finite fields. For polynomials of degree n over a finite field _q, the average-case complexity of our algorithm is an expected O(n^1 + o(1)log^2 + o(1)q) bit operations. Only for a negligible subset of polynomials of degree n our algorithm has a higher complexity of O(n^4 / 3 + o(1)log^2 + o(1)q) bit operations. This breaks the classical 3/2-exponent barrier for polynomial factorization over finite fields <cit.>.