A Class Of Continued Fraction Of Linear Type Lower Bound And Several Types Of Proxy Signature Scheme Design,

In this dissertation, we mainly study the lower bound for the linear form of continued fractions with the integer powers, and some 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 The lower bound for│A│=│β1f1+β2f2+α│was given, where y1=y(x1),y2=y(x2), x1 and x2 were positive integers, and that a,β1,andβ2 were algebraic numbers.2. According to the security analysis of a designated receiver proxy signature scheme,we present that Dai-scheme is insecure against the forgery attack, because of a hanging isolated factor.3. Using the bilinear pairing defined on elliptic curves, with the ideas of designated verifier signature scheme and proxy signature scheme, a new ID-based designated verifier proxy signature scheme is proposed. According to the security analysis, the scheme satisfies the security requirements.4. With the ideas of nominative signature scheme and proxy multi-signature scheme, a new Forward-secure nominative proxy multi-signature scheme is proposed, the scheme meets with the security requirements.