Hayder Raheem Hashim
DOI : 10.3844/jmssp.2014.304.308
Journal of Mathematics and Statistics
Volume 10, 2014
Cryptography is the science of using mathematics that's used to hide information or data that is being sent between participants in a way that prevents other people from reading it. The need of exchanging messages secretly promoted the creation of cryptosystems to enable receivers to interpret the exchanged information. In this study, a particular public key cryptosystem called Rabin Cryptosystem is presented considered with the help of Chinese Reminder Theorem. Since the decryption algorithm of the Rabin cryptosystem is based on computing square roots modulo n, where n = p.q where p and q are primes. This study suggests a modification of Rabin cryptosystem that can make the cryptosystem more immune against some attacks. This modification focuses on considering n = p. q. r where p, q and r are primes. This new modification of Rabin cryptosystem is called H-Rabin Cryptosystem. Also, some basic mathematical concepts are explained and it finally compares the H-Rabin Cryptosystem, RSA cryptosystem and Rabin cryptosystem in terms of security and efficiency. This H-Rabin cryptosystem is a public key cryptosystem where the private key is composed of three primes, p, q and r and a public key composed of n = p. q. r and it is based on the hardness of factoring. Therefore, this new modification can make the cryptosystem more immune against some future attacks.
© 2014 Hayder Raheem Hashim. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.