Pairing-based cryptosystems and key agreement protocols.

For a long time, pairings on elliptic curves have been considered to be destructive in elliptic curve cryptography. Only recently after some pioneering works, particularly the well-known Boneh-Franklin identity-based encryption (IBE), pairings have quickly become an important
tool to construct novel cryptographic schemes.
In this thesis, several new cryptographic schemes with pairings are proposed, which are both efficient and secure with respect to a properly defined security model, and some
relevant previous schemes are revisited.
IBE provides a public key encryption mechanism where a public key can be an arbitrary string such as an entity identifier and unwieldy certificates are unnecessary. Based on the Sakai-Kasahara key construction, an IBE scheme which is secure in the Boneh-Franklin IBE model is constructed, and two identity-based key encapsulation mechanisms are proposed. These schemes achieve the best efficiency among the existing schemes to date. Recently Al-Riyami and Paterson introduced the certificateless public key encryption (CL-PKE) paradigm, which eliminates the need of certificates and at the same time retains the desirable properties of IBE without the key escrow problem. The security formulation of CL-PKE is revisited and a strong security model for this type of mechanism is defined.
Following a heuristic approach, three efficient CL-PKE schemes which are secure in the defined strong security model are proposed. Identity-based two-party key agreement protocols from pairings are also investigated.
The Bellare-Rogaway key agreement model is enhanced and within the model several previously unproven protocols in the literature are formally analysed. In considering that the user identity may be sensitive information in many environments, an identity-based key agreement protocol with unilateral identity privacy is proposed.

Submitted in partial fulfilment of the requirenebts for the degree of Doctor of Philosophy at Middlesex University, London, United Kingdom.