| 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. |
