Classical and Quantum Algorithms for Exponential Congruences
نویسندگان
چکیده
Abstract. We discuss classical and quantum algorithms for solvability testing and finding integer solutions x, y of equations of the form af + bg = c over finite fields Fq. A quantum algorithm with time complexity q(log q) is presented. While still superpolynomial in log q, this quantum algorithm is significantly faster than the best known classical algorithm, which has time complexity q(log q). Thus it gives an example of a natural problem where quantum algorithms provide about a cubic speed-up over classical ones.
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