Fail-Stop Signatures And Multiple-Party Key Agreement Protocols

Elliptic curve public-key cryptography is the major research direction of modern cryptography. Digital signatures and key agreement are the two main fields of cryptography research and they have some important applications. In this thesis, it firstly presents the main branches of public-key cryptography, and then summarizes digital signatures which based on different problems and application backgrounds. Meanwhile it analyzes the current development situation of the key agreement.The signatures with special properties have wide application prospect, and the features of fail-stop signatures can protect customers in electronic payment system. A new fail-stop signature program based on elliptic curve discrete logarithm problem was proposed. The new protocol gives a one-time and multiple messages signatures. Furthermore, the security attributes are demonstrated, and then it shows how to achieve "fail-stop" about the two schemes. It can be considered as fully equivalent to handwritten signatures in which the signers are able to prove forgeries. Attributed to the difficulties of ECDLP and the short key of ECC, this program is safe, effective and practical.Key management, especially the key agreement is the chief topic of cryptography. The thesis reviews the classical Diffie-Hellman and Joux's protocols. On that basis, the new two-party and three-party key agreement protocol applying bilinear pairings were given. The proposed schemes resist man-in-the-middle attack. In addition, they can provide key confirmation, perfect forward secrecy, and key-comprise impersonation resilience, etc. After that the new protocols are expanded to group key agreement model in tree-form. The members in the group can be freely combined and generate the final session keys.