Contributions to pairing-based digital signatures

Nowadays, electronic communication plays a key role in the way people communicate in business or financial transactions. As e-commerce becomes more and more popular, the demand for digital signature is increasing rapidly. In 1976 Whitfield Diffie and Martin Hellman introduced the concept of digital signature [31] which is used to demonstrate the authenticity of a message or document. In 1977, Ronald Rivest, Adi Shamir and Len Adleman [66] proposed the notion of the RSA algorithm based on the factoring problem. In addition to the RSA signature, other signatures such as ElGamal signature [34], Rabin signature [65], Pairing-based signature [14], Undeniable signature [21] and others have been proposed by a number of different researchers. Due to the fact that users can enjoy properties such as authentication of the message, integrity of the message and non-repudiation of the message, digital signature has partially replaced the original ink on paper signatures. However, there exist a number of problems and potential attacks on digital signatures. It is observed that the majority of IBS schemes have the weakness of private key escrow. Additionally, existing solutions for security model could be made simpler and much more practical. In this thesis, two different pairing-based signatures: efficeint escrow free identity based signature [88] and (strong) multi-designated verifiers signatures secure against rogue key attack - are proposed to enhance the security of the pairing-based signature against a number of attacks. This thesis addresses two problems in the two different pairing-based signatures mentioned earlier and comes up with solutions that is neat, correct, secure and efficient.