The Research And Design Of Digital Signature Based On Bilinear Pairings

As the rapid development of E-commerce and E-government,digital signature technology is playing an increasingly important role in contemporary society, people study the digital signature has changed from the general signatures to the special signatures, and the digital signatures based on bilinear are in the system. Pairings is an important tool used to construct cryptographic protocols in recent years, it can be constructed by the Weil and Tate in elliptic curves . By pairing to construct a secure digital signature, has incomparable advantages of other methods, especially in a secure short signature, can greatly shorten the length of the signature. Bandwidth is limited for some occasions, its meaning is self-evident.This paper mainly focus on the digital signature based on bilinear and the digital signature of the group ,and launched a signature-related research, such as the short signature scheme and short group signature scheme, and we conducted a depth analys on the two related programs .The main research results are as follows:(1) Studyed the pairing, bilinear groups and the difficulties associated with the bilinear assumptions,and on this basis, the new program proposed the difficult issues involved assumptions.(2) Compared the general digital signatures with the short signature,and found that if you build a secure short signature scheme, in the case of authentication security, the signature length is shorter than the average digital signatures, and more efficient.(3) Analysised the BLS short signature scheme and the BB short signature scheme, and constructed a new short signature scheme,also made some improvements on this basis.Through the security analysis, show that the program is effective and can not be forged ,with a digital signature necessary security requirements.(4) Introduced the CZK group signature scheme and an improvement program of it, learn about the identity-based signature scheme on the construction method.Then study the BBS short group signature scheme and an improvement program of it in-depth.For the limitations of the random oracle model, we constructed a standard model of the short group signature scheme, and proved the security of this program. New group signature scheme is not only meet all the features, but also have higher efficiency and shorter length of the signature features.(5) For the application of group signature, we introduced some preliminary knowledge of electronic auction, and according to actual needs,we proposed a electronic auction scheme,which based on group signature ,also proved the security of the scheme fully.