Abstract
AbstractWe show that given the order of a single element selected uniformly at random from $${\mathbb {Z}}_N^*$$
Z
N
∗
, we can with very high probability, and for any integer N, efficiently find the complete factorization of N in polynomial time. This implies that a single run of the quantum part of Shor’s factoring algorithm is usually sufficient. All prime factors of N can then be recovered with negligible computational cost in a classical post-processing step. The classical algorithm required for this step is essentially due to Miller.
Funder
Swedish NCSA, Swedish Armed Forces
Publisher
Springer Science and Business Media LLC
Subject
Electrical and Electronic Engineering,Modelling and Simulation,Signal Processing,Theoretical Computer Science,Statistical and Nonlinear Physics,Electronic, Optical and Magnetic Materials
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