An ID-Based Public Key Cryptosystem based on Integer Factoring and Double Discrete Logarithm Problem

In 1984, Shamir [1] introduced the concept of an identity-based cryptosystem. In this system, each user needs to visit a key authentication center (KAC) and identify him self before joining a communication network. Once a user is accepted, the KAC will provide him with a secret key. In this way, if a user wants to communicate with others, he only needs to know the “identity” of his communication partner and the public key of the KAC. There is no public file required in this system. However, Shamir did not succeed in constructing an identity based cryptosystem, but only in constructing an identity-based signature scheme. In this paper, we propose an id based cryptosystem based on the integer factoring and double discrete logarithm problem and we consider the security against a conspiracy of some entities in the proposed system and show the possibility of establishing a more secure system. Key word: Public key Cryptosystem, Identity based Cryptosystem, Discrete Logarithm Problem, Double Discrete Logarithm Problem and Integer Factoring.