Open AccessJournal Article
Advances in composite integer factorization
6
TL;DR: In this research, a new method of integer factorization is proposed that will determine whether a given integer is prime or and its prime factors.
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Abstract: In this research we propose a new method of integer factorization. Prime numbers are the building blocks of arithmetic. At the moment there are no efficient methods (algorithms) known that will determine whether a given integer is prime or and its prime factors [1]. This fact is the basis behind many of the cryptosystems currently in use.
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Citations
Strategy for Algorithm Design in Factoring RSA Numbers
TL;DR: The article investigates the affection of the divisor-ratio of a RSA number to the efficiency of searching the number’s divisors in term of valuated binary tree and puts forward a framework for designing algorithms of fast factoring the RSA numbers.
A Parallel Probabilistic Approach to Factorize a Semiprime
TL;DR: An approach that can find out the small divisor of a semiprime by parallel computing that incorporates a deterministic search with a probabilistic search, requires less memory and can be implemented on ordinary multicore computers.
Algebraic approach to composite integer factorization
Aldrin W. Wanambisi,Shem Aywa,Cleophas Maende,Geoffrey Muchiri Muketha +3 more
- 01 Jan 2013
TL;DR: Aldrin W. Wanambisi and Shem Aywa as discussed by the authors at the University of Nairobi, N. Mt. Kenya, K.O box 553-50100, Kakamega, Kenya and Mt. Cleophas Maende School of Post Graduate Studies, Mount Kenya University, P.O Box 342-00100, Thika, Kenya.
Densification of Witnesses for Randomized Algorithm Design
Fudi Wang
TL;DR: Densification of witnesses for randomized algorithm design promotes the abundance of witnesses and facilitates factoring integers.
A New Approach Based on Parallel Probabilistic to Factorize a Semiprime
Jianhui Li
- 14 Jul 2019
TL;DR: A method for finding small divisors of semi-prime numbers by parallel computing, which combines deterministic search with probabilistic search, requires less memory and can be implemented on a common multi-core computer.
References
•Book
Elementary Number Theory
David M. Burton
- 01 Jan 1976
TL;DR: In this paper, the authors present a theory of divisibility theory in the Integers, which is based on the Fermat Conjecture of the Quadratic Reciprocity Law.
1.1K
Elementary number theory
TL;DR: The book as mentioned in this paper is designed for a first course in number theory with minimal prerequisites and is designed to stimulate curiosity about numbers and their properties, including almost a thousand imaginative exercises and problems.
809
•Dissertation
Integer factorization algorithms
Polona Bogataj
- 16 May 2011
TL;DR: The purpose of this thesis is to present different algorithms for natural number factorization, whose time complexity depends on the properties of the factorized number.
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