Abstract
The RSA cryptosystem is most commonly used for providing privacy and ensuring authenticity of digital data. 1'his system is based on the difficulty of integer factoring. Many attacks had been done, but none of them devastating. They mostly illustrate the dangers of improper use of RSA. Improper use implies many aspects, but here we imply the misuse of the parameters of RSA. Specially, sizes of parameters give strong effects on the efficiency and the security of the system. Parameters are also related each other. We analyze the relation of them. Recently many researchers are interested in side-channel attacks. We also investigate partial key exposure attacks, which was motivated by side-channel attacks. If a fraction of tile secret key bits is revealed, the private key will be reconstructed. We also study mathematical background of these attacks, solving modular multivariate polynomial equations.