Study On Bilinear Digital Signature Schemes

Bilinear is a popular system of digital password in recent years, and it is animportant tool to construct a digital signature scheme based on bilinear with theadvantages of short key, high safety and rapid implementation. Bilinear mapping isfrom hypersingular elliptic curves of and being paired, many of the originalpassword system based on the discrete logarithm problem of cryptography, can betransplanted to the hypersingular elliptic curves, which can obtain the correspondingbased on Hyperelliptic Curve Cryptosystem and improve efficiency, comparing withthe original cryptosystem.This essay got some new scheme through the analysis on the original schemeand the research based on blind signature, proxy signature, the signature of themultiple signature and group:1.Partially certificateless blind signature scheme based on pairings, not only hasthe advantage of certificateless public key cryptography, but also meet thecharacteristics of partially blind signature, which has high efficiency, even can play arole in the electronic cash and voting application. And based on the design, blindsignature scheme is applied to multiple signatures, getting the order of multiplepartially blind signature and broadcasting multiple partially blind signature. Thus thesignature has some special properties and a better application in practice;2. With forward secure proxy signature scheme based on bilinear pairings canensure the power of proxy signers, and effectively avoid the misuse of proxy signerpower. As it has a certain timeliness, it can ensure both the original signer’s and theproxy signer’s interest, raising the safety of signature scheme. Then this program isapplied to multiple signatures and gets a multi-proxy signature scheme, namely"generation". So it can solve the problem of signature scheme, when it requires a lotof proxy signers. This signature scheme thus has certain practical significance;3. Signcryption scheme for the group based on the bilinear, adding the idea ofsigncryption, that is, through the encryption and decryption algorithm, reduces thecomputational complexity and improves the efficiency. In this signature scheme, thegroup public key and signcryption length is independent of the group members,which is a constant number, i.e. it can not affect because how much we increase ordelete a group member, so we can conclude this signature scheme also has important practical significance.