Research Of Digital Signatures Based On Bilinear Pairings

Information security is one of the most important problems in modern Information society and becomes a new important subject in the information science. Digital signature, which can provide authentication, integrity, and non-repudiation, is one of the key techniques of information security and plays an important role in E-commerce and E-governance. As the deepening of digital signature research and the rapid development of E-commerce and E-governance, the standard signature, which is a simple simulacrum of handwritten signature, can not meet the practical need anymore. Thus, making research on the digital signatures with additional properties becomes a main research direction in digital signatures.Bilinear pairing, derived from Weil pairing or Tate pairing of elliptic curves, is becoming an important tool for constructing cryptographic protocols in recent years. There are two advantages of protocols from bilinear pairing: (1) Constructions of cryptographic protocols which can not be constructed using other techniques; (2)Constructions of cryptographic protocols which can be constructed using other techniques, but for which bilinear pairing provides improved functionality.The two main contributions of this thesis are as follows:1. The author proposes two verifiably committed signature schemes which can be used for optimistic fair exchange of BLS signatures. Their security is proved under the Computational Diffie-Hellman assumption in the random oracle model. Additionally, the second scheme is abuse-free and the proof of its abuse-freeness is based on a new type of the extension of Computational Diffie-Hellman assumption.2. The author propose a new and more generic paradigm(than Boneh et al. 's one)which modularly transforms any weakly unforgeable signature scheme into a strongly unforgeable one. Then, by applying the paradigm to the Waters signature scheme, the author constructs a new strongly unforgeable signature scheme which is provably secure under the CDH assumption over bilinear groups in the standard model. In the signature scheme, the major computation can be performed off-line.