A Public Key Cryptosystem based on number theory

Public Key Cryptosystem came into existence after 1975. Since then a large number of research has been conducted in this area. It is based on number theory and exploits the features of computationally hard problems, namely integer factorization, discrete logarithmic problem to name a few. In this paper we describe a public-key cryptosystem. The basis of the design is derived from first version of Euler's Theorem. Apart from exponentiation and residue to a modulus, it is also based on some base and remainder. The remainder plays a crucial role on the selection of the exponents. The base is used to generate the residue to a modulus. Both the base and the remainder make cryptanalysis tough.