中文摘要：

基于线性假设下的Cramer-Shoup加密方案和SDH假设，提出一种新的SDH问题的零知识证明协议，并基于此协议构造了一种在Bellare-Micciancio-Warinshi模型下可证明安全的短群签名方案．该方案具有IND-CCA2完全匿名性，允许攻击者在攻击完全匿名性时提问打开预言机．签名的长度仅为1704bits．

英文摘要：

In CRYPTO 2004, a short group signature is proposed by Boneh, Boyen ancl Shacham, which is based on strong Diffie-Hellman（SDH） assumption and Decision Linear assumption. Thereafter it is denoted BBS. Only chosen plaintext attack（CPA） full-anonymity is achieved in BBS short group signature for CPA secure in linear encryption. In this case, adversary could not query an open oracle. However, when adversaries try to break the notion of chosen ciphertext attack（IND-CCA2） full-anonymity, they have the ability to query an open oracle in the current and strongest security model for group signatures. Hence adversaries can obtain the signer identity of the queried signature. This paper presents a new zero-knowledge protocol for SDH, which based on Cramer-Shoup encryption from the linear assumption. Using this protocol as a building block, a new short group signature is constructed in this paper, which is provable secure in the Bellare-Micciancio-Warinshi model. The scheme is of IND-CCA2-full-anonymity, which allows adversary querying open oracle when trying to attack the anonymity notion. And the signature is only 1704 bits in size.