Fast Approach to Factorize Odd Integers: An algorithm Based Study | Chapter 7 | Current Topics on Mathematics and Computer Science Vol. 10

 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 2^au +1 or 2^au -1 with u being an odd integer and α being a positive integer and the other divisor p satisfies 1 < p < 2^a +1 or 2^a +1 < p <2^a+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.

Author(s) Details

Xingbo Wang
Department of Mechatronic Engineering, Foshan University, Foshan City, PRC, 528000, China and State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China and Guangdong Engineering Center of Information Security for Intelligent Manufacturing System, China.

Junjian Zhong
Department of Mechatronic Engineering, Foshan University, Foshan City, PRC, 528000, China.

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