Cryptographic Schemes based on Elliptic Curve Pairings

by Sattam S. Al-Riyami

Abstract:

This thesis introduces the concept of certificateless public key
cryptography (CLPKC). Elliptic curve pairings are then used to
make concrete CL-PKC schemes and are also used to make other
efficient key agreement protocols.

CL-PKC can be viewed as a model for the use of public key cryptography
that is intermediate between traditional certificated PKC and ID-PKC.
This is because, in contrast to traditional public key cryptographic
systems, CL-PKC does not require the use of certificates to guarantee
the authenticity of public keys. It does rely on the use of a trusted
authority (TA) who is in possession of a master key. In this
respect, CL-PKC is similar to identity-based public key
cryptography (ID-PKC). On the other hand, CL-PKC does not suffer
from the key escrow property that is inherent in ID-PKC.
Applications for the new infrastructure are discussed.

We exemplify how CL-PKC schemes can be constructed by constructing
several certificateless public key encryption schemes and
modifying other existing ID based schemes. The lack of
certificates and the desire to prove the schemes secure in the
presence of an adversary who has access to the master key or has
the ability to replace public keys, requires the careful
development of new security models. We prove that some of our
schemes are secure, provided that the Bilinear Diffie-Hellman
Problem is hard.

We then examine Joux’s protocol, which is a one round, tripartite
key agreement protocol that is more bandwidth-efficient than any
previous three-party key agreement protocol, however, Joux’s protocol
is insecure, suffering from a simple man-in-the-middle attack. We
show how to make Joux’s protocol secure, presenting several tripartite,
authenticated key agreement protocols that still require only one round
of communication. The security properties of the new protocols are
studied. Applications for the protocols are also discussed.