Journal of Information Security Research Ramesh ch, K Venugopal Rao, D Vasumathi 9 1 2018 http://www.dline.info/jisr/fulltext/v9n1/jisrv9n1_2.pdf A Public-Key System (especially Identity-Based Encryption) is said to be secure if it is proved to be secure against simulation studies, taking into account the purpose of the attacker and the model used. Among the goals there are indistinguished IND and semantic goal, regarding the models, we quote Chosen Plaintext Attack (CPA),Chosen Ciphertext Attack (CCA). Their combination gives INDistinguishability under Chosen Plaintext Attack (IND-CPA), semantic-CPA, semantic- CCA, IND-CCA. The study considered as strong and concretizing for ideal security is IND-CCA, for the IBE we talk about IND-ID-CCA (also: semantics-ID-CPA, semantics-ID-CCA, IND-ID-CPA) . This IND-ID-CCA (as well as the others) belongs to a full domain whose identity to attack is declared in the challenge. This IND-ID-CCA (as well as the others) belongs to a full domain whose identity to attack is declared in the challenge. A so-called weak type is introduced in 2003 by Canetti et al [1] and is called selective-ID. In this model, the target identity to be attacked is declared in the beginning that is in the Setup. It is proved in [2] that the transition from selective ID to a complete domain requires a multiplication by N (produces a degradation in the security). In spite of this weakness, in Eurocrypt 2004 Boneh and Boyen [2] proposed two crypto systems under this type, these are the only ones known in the literature drawn up in the same type. The first is a HIBE based on the DBDHP (Decisional of Diffie and Hellman Problem) problem and under the Commutative Blinding approach it is known by BB1. While the second is an IBE Under the Exponent-Inversion approach named BB2, it is based on Dq-BDHIP (Decisional q- Invertible of Bilinear Diffie and Hellman Problem). By combining the idea of the inverse used in BB2 and remaining in the Commutative Blinding approach,In this paper we will propose our New IBE scheme [5] which will be efficient than BB1 (IBE version [4]) and even BB2.