An ID-based cryptographic mechanisms based on GDLP and IFP

In 1984, Shamir introduced the concept of an identity-based cryptosystem. In this system, each user needs to visit a key authentication center (KAC) and identify himself 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 under the security assumptions of the generalized discrete logarithm problem and integer factorization problem. We consider the security against a conspiracy of some entities in the proposed system and show the possibility of establishing a more secure system.