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International Journal of Computer Network and Information Security(IJCNIS)

ISSN: 2074-9090 (Print), ISSN: 2074-9104 (Online)

Published By: MECS Press

IJCNIS Vol.5, No.9, Jul. 2013

Improved Trial Division Technique for Primality Checking in RSA Algorithm

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Author(s)

Kumarjit Banerjee, Satyendra Nath Mandal, Sanjoy Kumar Das

Index Terms

Improved Trial Division, RSA Algorithm, Primality Checking, Pseudo primes, 210k Approach

Abstract

The RSA cryptosystem, invented by Ron Rivest, Adi Shamir and Len Adleman was first publicized in the August 1977 issue of Scientific American. The security level of this algorithm very much depends on two large prime numbers. To check the primality of large number in personal computer is huge time consuming using the best known trial division algorithm. The time complexity for primality testing has been reduced using the representation of divisors in the form of 6n±1. According to the fundamental theorem of Arithmetic, every number has unique factorization. So to check primality, it is sufficient to check if the number is divisible by any prime below the square root of the number. The set of divisors obtained by 6n±1 form representation contains many composites. These composite numbers have been reduced by 30k approach. In this paper, the number of composites has been further reduced using 210k approach. A performance analysis in time complexity has been given between 210k approach and other prior applied methods. It has been observed that the time complexity for primality testing has been reduced using 210k approach. 

Cite This Paper

Kumarjit Banerjee, Satyendra Nath Mandal, Sanjoy Kumar Das,"Improved Trial Division Technique for Primality Checking in RSA Algorithm", IJCNIS, vol.5, no.9, pp.51-57,2013. DOI: 10.5815/ijcnis.2013.09.07

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