Integer factorization: Solution via algorithm for constrained discrete logarithm problem

Document Type

Article

Publication Date

9-22-2009

Abstract

Problem statement: During the last thirty years many public-key cryptographic protocols based on either the complexity of integer factorization of large semiprimes or the Discrete Logarithm Problem (DLP) have been developed. Approach: Although several factorization algorithms with sub-exponential complexity had been discovered, the recent RSA factoring challenge demonstrated that it was still necessary to use several thousand computers working in a coordinated effort for several months to factor an integer n that was a product of two primes. Results: In this study it was demonstrated how to find integer factors of n using an algorithm for a constrained DLP. Several numerical examples illustrate details of the algorithms. One of these algorithms has O(√n) complexity; and, if the search was balanced, it has complexity O(n1/3/log1/αn), where alpha>1. Conclusion/Recommendations: A specific algorithm is a method that after a finite number of well-defined and executable steps provably delivers a solution to a class of problems. © 2009 Science Publications.

Identifier

70349164147 (Scopus)

Publication Title

Journal of Computer Science

External Full Text Location

https://doi.org/10.3844/jcssp.2009.674.679

ISSN

15493636

First Page

674

Last Page

679

Issue

9

Volume

5

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