Modified Miller-Rabin primality test algorithm to detect prime numbers for generating RSA keys

A prime number is a number that is only divisible by one and itself, which is essentially saying that it has no divisor. Prime numbers are important in the security field because many encryption algorithms are based on the fact that it is very easy to multiply two large prime numbers and get the...

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Main Author:	Shereek, Balkees Mohamed
Format:	Thesis
Language:	English
Published:	2016
Subjects:	Data encryption (Computer science) - Mathematical models Algorithms
Online Access:	http://psasir.upm.edu.my/id/eprint/69356/1/FSKTM%202016%2021%20IR.pdf
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id	my-upm-ir.69356
record_format	uketd_dc
spelling	my-upm-ir.693562019-07-10T03:40:32Z Modified Miller-Rabin primality test algorithm to detect prime numbers for generating RSA keys 2016-06 Shereek, Balkees Mohamed A prime number is a number that is only divisible by one and itself, which is essentially saying that it has no divisor. Prime numbers are important in the security field because many encryption algorithms are based on the fact that it is very easy to multiply two large prime numbers and get the result, while it is extremely computerintensive to do the reverse. The Rivest-Shamir-Adleman algorithm (RSA) is one of the most well-known and strongest public key cryptography algorithms. The security of the RSA depends on the two prime numbers namely p and q and to generate them is an extremely time consuming process (Fu and Zhu, 2008). An efficient method for generating large random prime numbers within shortest time is thus a crucial challenge for researchers (Bahadori et al., 2010; Saveetha and Arumugam, 2012). The objective of this study is to reduce the time taken in finding prime numbers p and q for RSA. To achieve the objective, the Miller-Rabin primality test was modified by adding few tests in the original Miller-Rabin. The prime numbers with the size of 256, 512, and 1024 bits are generated using the proposed modified algorithm. The performance of the proposed modified Miller-Rabin was analysed in terms of the time taken to detect the prime numbers and compare the time taken for generating the prime numbers using original Miller-Rabin method. The comparison between the original Miller- Rabin and the modified Miller-Rabin primality test methods show the difference of time to generate prime numbers and the modified method shown the better results. The study also reviewed previous works and the modified Miller-Rabin primality test method has shown the better results in compared to them. Data encryption (Computer science) - Mathematical models Numbers, Prime Algorithms 2016-06 Thesis http://psasir.upm.edu.my/id/eprint/69356/ http://psasir.upm.edu.my/id/eprint/69356/1/FSKTM%202016%2021%20IR.pdf text en public masters Universiti Putra Malaysia Data encryption (Computer science) - Mathematical models Numbers, Prime Algorithms
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Data encryption (Computer science) - Mathematical models Data encryption (Computer science) - Mathematical models Algorithms
spellingShingle	Data encryption (Computer science) - Mathematical models Data encryption (Computer science) - Mathematical models Algorithms Shereek, Balkees Mohamed Modified Miller-Rabin primality test algorithm to detect prime numbers for generating RSA keys
description	A prime number is a number that is only divisible by one and itself, which is essentially saying that it has no divisor. Prime numbers are important in the security field because many encryption algorithms are based on the fact that it is very easy to multiply two large prime numbers and get the result, while it is extremely computerintensive to do the reverse. The Rivest-Shamir-Adleman algorithm (RSA) is one of the most well-known and strongest public key cryptography algorithms. The security of the RSA depends on the two prime numbers namely p and q and to generate them is an extremely time consuming process (Fu and Zhu, 2008). An efficient method for generating large random prime numbers within shortest time is thus a crucial challenge for researchers (Bahadori et al., 2010; Saveetha and Arumugam, 2012). The objective of this study is to reduce the time taken in finding prime numbers p and q for RSA. To achieve the objective, the Miller-Rabin primality test was modified by adding few tests in the original Miller-Rabin. The prime numbers with the size of 256, 512, and 1024 bits are generated using the proposed modified algorithm. The performance of the proposed modified Miller-Rabin was analysed in terms of the time taken to detect the prime numbers and compare the time taken for generating the prime numbers using original Miller-Rabin method. The comparison between the original Miller- Rabin and the modified Miller-Rabin primality test methods show the difference of time to generate prime numbers and the modified method shown the better results. The study also reviewed previous works and the modified Miller-Rabin primality test method has shown the better results in compared to them.
format	Thesis
qualification_level	Master's degree
author	Shereek, Balkees Mohamed
author_facet	Shereek, Balkees Mohamed
author_sort	Shereek, Balkees Mohamed
title	Modified Miller-Rabin primality test algorithm to detect prime numbers for generating RSA keys
title_short	Modified Miller-Rabin primality test algorithm to detect prime numbers for generating RSA keys
title_full	Modified Miller-Rabin primality test algorithm to detect prime numbers for generating RSA keys
title_fullStr	Modified Miller-Rabin primality test algorithm to detect prime numbers for generating RSA keys
title_full_unstemmed	Modified Miller-Rabin primality test algorithm to detect prime numbers for generating RSA keys
title_sort	modified miller-rabin primality test algorithm to detect prime numbers for generating rsa keys
granting_institution	Universiti Putra Malaysia
publishDate	2016
url	http://psasir.upm.edu.my/id/eprint/69356/1/FSKTM%202016%2021%20IR.pdf
_version_	1747812687457288192

Modified Miller-Rabin primality test algorithm to detect prime numbers for generating RSA keys

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