Fermat Factorization using a Multi-Core System

Factoring a composite odd integer into its prime factors is one of the security problems for some public-key cryptosystems such as the Rivest-Shamir-Adleman cryptosystem. Many strategies have been proposed to solve factorization problem in a fast running time. However, the main drawback of the algor...

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Vydané v:International journal of advanced computer science & applications Ročník 11; číslo 4
Hlavní autori: Bahig, Hazem M., M., Hatem, Kotb, Yasser
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: West Yorkshire Science and Information (SAI) Organization Limited 2020
Predmet:
Algorithms
Computer systems
Computing time
Cryptography
Factorization
Integers
Parameters
ISSN:2158-107X, 2156-5570
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Abstract Factoring a composite odd integer into its prime factors is one of the security problems for some public-key cryptosystems such as the Rivest-Shamir-Adleman cryptosystem. Many strategies have been proposed to solve factorization problem in a fast running time. However, the main drawback of the algorithms used in such strategies is the high computational time needed to find prime factors. Therefore, in this study, we focus on one of the factorization algorithms that is used when the two prime factors are of the same size, namely, the Fermat factorization (FF) algorithm. We investigate the performance of the FF method using three parameters: (1) the number of bits for the composite odd integer, (2) size of the difference between the two prime factors, and (3) number of threads used. The results of our experiments in which we used different parameters values indicate that the running time of the parallel FF algorithm is faster than that of the sequential FF algorithm. The maximum speed up achieved by the parallel FF algorithm is 6.7 times that of the sequential FF algorithm using 12 cores. Moreover, the parallel FF algorithm has near-linear scalability.
AbstractList Factoring a composite odd integer into its prime factors is one of the security problems for some public-key cryptosystems such as the Rivest-Shamir-Adleman cryptosystem. Many strategies have been proposed to solve factorization problem in a fast running time. However, the main drawback of the algorithms used in such strategies is the high computational time needed to find prime factors. Therefore, in this study, we focus on one of the factorization algorithms that is used when the two prime factors are of the same size, namely, the Fermat factorization (FF) algorithm. We investigate the performance of the FF method using three parameters: (1) the number of bits for the composite odd integer, (2) size of the difference between the two prime factors, and (3) number of threads used. The results of our experiments in which we used different parameters values indicate that the running time of the parallel FF algorithm is faster than that of the sequential FF algorithm. The maximum speed up achieved by the parallel FF algorithm is 6.7 times that of the sequential FF algorithm using 12 cores. Moreover, the parallel FF algorithm has near-linear scalability.
Author Kotb, Yasser
Bahig, Hazem M.
M., Hatem
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Computer systems
Computing time
Cryptography
Factorization
Integers
Parameters
Title Fermat Factorization using a Multi-Core System
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