With Linear-type Lower Bound Of The Fraction Of The Number Of Identity-based Signatures,

In this dissertation, we studied the lower bound for the linear form of logarithms of continued fraction with positive integer power and several identity-based signature schemes. The main achievements are as follows:1.Let{an} be a given sequence of positive integers, and x be a rational number. Define the function with the continued fractions as and the lower bound for the linear form of continued fraction was given, whereαandβwere the value at two different points of positive integers of the function, k and l were non-zero integers,C0 and c4 were constants, and2.Through the research of some identity-based proxy blind signature scheme which were based on bilinear pairing, we found that dishonest PKG were free to forge signatures. Based on this problem, this paper proposed an identity-based proxy blind scheme without trusted PKG. Security was analyzed, the result showed that this scheme was secure.3.Introduced the concept of threshold signature, based on linear pairing, threshold signature introduced into proxy blind signature scheme, and put forward an identity-based threshold proxy blind signature scheme.4.Combined with proxy multi-signature and blind signature, identity-based proxy multiple blind signature scheme was proposed, and the security was given.5.Based on the status of the signature sign and ring signature,with proxy signatures, ring signatures and signcryption together,to design an identity-based proxy ring signcryption scheme, and gave proof of the safety of the program.