Improving the Success Probability for Shor's Factoring Algorithm

Abstract

Given n=p*q with p and q prim and y in Z_{p*q}^*. Shor's Algorithm computes the order r of y, i.e. y^r=1 (mod n). If r=2k is even and y^k \ne -1 (mod n) we can easily compute a non trivial factor of n: gcd(y^k-1,n). In the original paper it is shown that a randomly chosen y is usable for factoring with probabily {1/2}. In this paper we will show an efficient possibility to improve the lower bound of this probability by selecting only special y in Z_n^* to {3/4}, so we are able to reduce the fault probabilty in the worst case from {1/2} to {1/4}.