An ID-based Beta Cryptosystem using Generalized Discrete Logarithm Problem and Integer Factorization Problem

In a modern open network system, data security technologies such as cryptosystems, signature schemes, etc., are indispensable for reliable data transmission. In particular, for a large-scale network, ID-based systems such as the ID-based cryptosystem, the ID-based signature scheme, or the ID-based key distribution system are among the better countermeasures for establishing efficient and secure data transmission systems. The concept of an ID-based cryptosystem has been proposed by Shamir [1], and it is advantageous to public-key cryptosystems because a large public-key file is not required for such a system. This paper proposes an ID-based beta cryptosystem under the security assumptions of the generalized discrete logarithm problem and integer factorization problem, which is one of the earliest realizations in Shamir's sense. Furthermore, we consider the security against a conspiracy of some users in the proposed system, and show the possibility of establishing a more secure system.