ABSTRACT
This chapter introduces the concept of Boneh and Boyen’s identity based encryption scheme. It introduces the preliminaries starting from the security model for selective Identity-Based Encryption (IBE) and the formal construction of the Boneh and Boyen scheme. Waters’ scheme presents fully (adaptively) secure solutions based on static assumptions in the standard model through hybrid games. On the other hand, the Waters’ proof methodology allows us to easily provide fully secure proof, it also raises a problem of efficiency degradation. In 2004, Boneh and Boyen proposed an efficient hierarchical identity based encryption system that is selective identity secure without random oracles based on the Decisional Bilinear Diffie-Hellman (DBDH) assumption. In particular, this implies an efficient selective identity, chosen ciphertext secure IBE based on DBDH without random oracles.
