The distribution of solutions to xy = N mod a with an application to factoring integers

Details The distribution of solutions to xy = N mod a with an application to factoring integers The distribution of solutions to xy = N mod a with an application to factoring integers

2006-10-20

arxiv.org/abs/math/0610612v4

Mathematics

Number Theory

13 pages

Scientific paper

We consider the uniform distribution of solutions $(x,y)$ to $xy=N \mod a$,
and obtain a bound on the second moment of the number of solutions in squares
of length approximately $a^{1/2}$. We use this to study a new factoring
algorithm that factors $N=UV$ provably in $O(N^{1/3+\epsilon})$ time, and
discuss the potential for improving the runtime to sub-exponential.

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