The Algorithm Design And Analysis Of Digital Signature With Special Nature

Delegation of signing right is a common issue in the real life. Certificateless signature which is actually a special kind of digital signature can provide a solution to such an issue. In this thesis,we discuss several certificateless proxy signatures and analyze their security in details. Moreover, we design a secure and efficient verifiably encrypted signature scheme. The major contributions are as follows:1. We cryptanalyze a certificateless signature scheme presented by Xu et al. and a certificateless proxy signature scheme presented by Fan et al. We show that Xu's scheme is universally forgeable, and in Fan's scheme, an original signer disclosed his private key when he delegated his signing ability to a proxy signer. Furthermore, we point out Fan's scheme cannot resist a public-key replacement attack. Our attack shows that anyone who replaces an original signer's public key and a proxy signer's public key can forge valid proxy signatures on behalf of the proxy signer without knowledge of the proxy signer's proxy private key.2. In order to design a secure and efficient verifiably encrypted signature scheme, we first propose a new digital signature scheme under the Square Computational Diffie-Hellman assumption. This scheme is provably secure in the random oracle model. And then, based on this signature scheme, a blind verifiably encrypted signature (BVES) scheme is presented in this paper. The BVES scheme enjoys desirable properties of unforgeability and opacity. Compared with existing VES schemes, our scheme's computational cost is lower and the whole operation only requires two pairing evaluations and five scalar multiplications. The size of the signature generated by our BVES is only 320 bits. So it can be used in environments with stringent bandwidth constraints.