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 communicatio...

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 communicatio...

The Discrete Logarithm Problem is at the base of the famous Diffie Hellman key agreement algorithm and many others. The key idea behind Diffie Helmann is the usage of the Discrete Logarithm function in (Z/pZ)∗ as a trap door function. The Discrete Logarithm function output in (Z/pZ)∗ seems to escape to any attempt of finding some sort of pattern. Nevertheless some new characterization will be i...