A study of Factoring Algorithms related to the RSA Cryptosystems

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Date
2008
Authors
Mohamed, Norliza
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Abstract
Cryptography is referred to the study of methods for sending messages in secret so that the intended recipient can remove the disguise and read the message. Now, this cryptography is extremely useful. In 1977, Ronald Rivest, Adi Shamir and Leonard Adleman with the initial of their surnames RSA were publicly a RSA Cryptosystem. This RSA Cryptosystem is a public-key cryptosystem that offers both encryption and digital signatures which is more secure. RSA cryptosystem relies very much on the length of the prime numbers used as well as the effectiveness of the available integer factoring algorithms. In this thesis several factoring algorithms and primality tests related to the RSA cryptosystem are discussed. Some examples are given as to indicate the underlying mathematical concepts used m the process. A mild programmmg usmg MATHEMATICA were also carried out for primality test and factoring composite numbers into primes. Some challenges and results on the latest development in integer factorization are shown and discussed. It is possible that new factoring algorithms may be developed in the future which once again targeted primes with certain properties.
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Keywords
RSA Cryptosystems , Factoring Algorithms
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