Abstract: Based on Linear Cramer-Shoup encryption, a new short group signature is proposed. The anonymity property of this scheme is secure against adaptive chosen-ciphertext attacks (CCA2), which allows the adversary to open the signature when trying to break the anonymity notion. Using this group signature as a building block, a secure electronic auction scheme is designed. Under the same security conditions, the scheme has sizes of signature, group public key, signing key, register key and tracing key 1／14, 1／7, 1／17, 1／40 and 1／4 those of the scheme based on the RSA problem. Compared with the pairing-based scheme in which the bidder’s anonymity is CPA secure, the complexities of communication and computation in this paper are approximate to those in the former, but the CCA2-full-anonymity of bidders is achieved in this new scheme.

Key words: electronic auction, group signature, linear Cramer-Shoup encryption, full-anonymity