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Title:
Shor’s Algorithm and Factoring: Don’t Throw Away the Odd Orders
Authors: Anna Johnston
Abstract:Shor’s algorithm factors an integer N in two steps. The quantum step computes the order of a\bmod{N} where a is relatively prime to N. The classical step uses this order to factor N. Descriptions of the classical step require the order, s, to be even and that a^{s/2}\not\equiv -1\bmod{N}. If s is odd or a^{s/2}\equiv -1\bmod{N}, then the quantum step is repeated. This paper describes how each prime divisor of the order s, not just 2, can be used to factor N.
ePrint: https://eprint.iacr.org/2017/083
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