Transcendence Of Number And Some Blind Signature Schemes With Message Recovery

In this dissertation, we mainly study the lower bound for the linear form of continued fraction logarithm with a type of binomial function, and some blind signature schemes with message recovery. The main achievements are as follows:1. Let{αn(x)}be a given function sequence of binomial,α,βbe the values of y=f(x) at two different integral points, k,l be integers not both zero. Define the function with continued fraction as the correlation properties of this function were studied, and the lower bound for∧= k logα+l logβwas given, which combined with the related knowledge about continued fraction and algebraic number.2. Based on the study of a designated verifier proxy blind signature scheme with message recovery, the paper proposes a new forward secure designated verifier cooperative blind signature scheme with message recovery by combining the concept of forward security. In this scheme, the signature is completed together by the signature sponsor and the signature partner. The scheme can be realized even if all the signers'signature keys are leaked, the attacker can not forged the signature of the previous stage, previous generated signature remain valid.3. Based on the study of one of the multi-signature schemes proposed by Abound, analyses the security of this scheme and gives a new-improvement scheme. Message in the new scheme can be transmitted secretly and must be recovered by the designated verifier. The analysis shows that the new improvement scheme is security.4. Show that the new threshold signature scheme based on modular secret sharing which proposed by Xie et al. is insecure. Any t signers who conspire with DC can forge a valid threshold signature and frame others, and any less than t individuals who conspire with DC can forge a valid threshold signature. To overcome the weakness, a modification to their scheme can satisfy the security requirement.