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Cryptography, the science of encryption, plays a central role in mobile phone communications, pay-tv, e-commerce, sending private emails, transmitting financial information, security of ATM cards, computer passwords, electronic commerce digital signature and touches on many aspects of our daily lives. RSA cryptosystem is the most commonly used public key cryptosystem. It is the first public key cryptosystem. The strength of this cryptosystem is based on the larger key size. There are many algorithms and variants of RSA. But, it is steal a burning topic of research. Because the thrust to store data secret is never going to end. In this book, we have proposed a literature review of some modern variants of the RSA algorithm. All the algorithms have been analyzed. Their merits and demerits are also discussed. In digital era, the data continuously moves on the network. So the personal or confidential record is required to be protected from the outside world. So there is a need to develop a zero tolerant security algorithm. In this book, proposed a modified RSA algorithm. The proposed version is taking less time in data decryption.