The dual-chain architecture of China's regional equity markets has been largely established but remains in an exploratory phase. As the core execution unit within this architecture, smart contracts must be strictly controlled in terms of access permissions, as unauthorized invocation may lead to significant losses. However, traditional access control methods pose a risk of exposing user identity information, thereby compromising user privacy. This paper proposes an anonymous access control scheme for smart contracts that preserves user identity privacy. By leveraging group signature techniques, invocation credentials are generated using private signing keys issued and authorized by a system administrator, enabling effective permission management and user supervision. The scheme also utilizes blockchain technology to support permission revocation. In addition, the signature and verification processes of the BBS short group signature mechanism are optimized to enhance overall performance, making the scheme more suitable for integration with smart contracts. Experimental results demonstrate that the proposed scheme outperforms both the original BBS short group signature algorithm and the latest related works, meeting the high-security and high-performance requirements of business contracts in regional equity markets.