Fast Approach to Factorize Odd Integers with Special Divisors
- 1 Foshan University, China
Published On: 27 January 2020
Copyright: © 2020 Xingbo Wang and Junjian Zhong. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
The paper proves that an odd composite integer N can be factorized in O((log2N)4) bit operations if N = pq, the divisor q is of the form 2αu +1 or 2αu-1 with u being an odd integer and α being a positive integer and the other divisor p satisfies 1 < p ≤ 2α+1 or 2α +1 < p ≤ 2α+1-1. Theorems and corollaries are proved with detail mathematical reasoning. Algorithm to factorize the odd composite integers is designed and tested in Maple. The results in the paper demonstrate that fast factorization of odd integers is possible with the help of valuated binary tree.
- Integer Factorization
- Binary Tree