The distribution of solutions to xy = N mod a with an application to factoring integers
Michael Rubinstein
Abstract
We consider the uniform distribution of solutions (x,y) to xy=N a, and obtain a bound on the second moment of the number of solutions in squares of length approximately a1/2. We use this to study a new factoring algorithm that factors N=UV provably in O(N1/3+ε) time, and discuss the potential for improving the runtime to sub-exponential.
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