Blind signature is a special anonymous technique; it can realize the anonymity of the signed message. A common blind signature is achieved in PKI and ID-based cryptography. However, self-certified signature scheme is a better choice than that in traditional public key system and ID-based cryptography, since it omits key escrow problem of ID-based crypto-system and avoids complex certificate management of traditional PKI. In the work, we first formalized the security models of self-certified blind signature by classifying its adversary types. Then, we proposed a concrete instance. And we also show that the proposed scheme is provably secure in the random oracle models and the security of the scheme is closely related to a extended security assumption: q-SDH+CDH assumption which is provided by us. And we show that the proposed scheme is very efficient in terms of computational costs of generation and verification of a signature. Because no pairing operator is required in the signing phase of our scheme, thus our blind signature scheme is very efficient in terms of computational cost.

A new electronic auction scheme is proposed based on group signatures and partially blind signatures. At the same security strengthen, an optimization was done on the processes of electronic auction scheme and the dependence on trusted third party was reduced, moreover, multiple goods is auctioned at the same time, therefore, this scheme suited to large-scale electronic auction. Furthermore, due to application of vickrey auctions, the principle of optimal allocation of goods is easily satisfied.

Chameleon signatures simultaneously provide the properties of non-repudiation and non-transferability for the signed message. However, the initial constructions of chameleon signatures suffer from the key exposure problem of chameleon hashing. This creates a strong disincentive for the recipient to forge signatures, partially undermining the concept of non-transferability. Recently, some specific constructions of key-exposure free chameleon hashing based on various assumptions are presented.In this paper, we present some security flaws of the key-exposure free chameleon hash scheme based on factoring [10]. Besides, we propose an improved chameleon hash scheme without key exposure based on factoring which enjoys all the desired security notions of chameleon hashing.