Research On Cryptosystems Based On The Pairings

In 1989 Neal Koblitz first put forward the theory of Hyperelliptic curve cryptosystems (HECC). Compared to ECC, the base-field of HECC is smaller than that of ECC with the same level of security. And therefore, the relative theory of HECC attracts much important attention in the last 10 years.Joux initially proposed a one-round three-part Deffie-Hellman key change protocol. There has been a lot of efficient implementation of pairings on elliptic curves. The applications of pairings are popular issues in the last years, but there are many idiographic problems which are not settled yet. In this dissertation, the main works of the author is follows:(1) The encryption and decryption of the ECC could be actualized in Maple.(2) An efficient ID-based digital signature with message recovery is proposed based on the bilinear paring.