Star-Topological Encryption: Talking to the Sever but Hiding Identities to Others ^∗

In this paper, we propose the notion of Star-Topological encryption that enables some clients confidentially talking to a server but without revealing their identities to others. Then, an encryption scheme is constructed to achieve this cryptosystem based on non-abelian groups. The proposal realizes identity-based encryption and identity authenticity, simultaneously. In this encryption system, both the encryptions and decryptions of two sides of the communications are relying on secret key. Therefore, the encryption/decryption algorithms employ the idea of symmetric key cryptosystem. Meanwhile, the client's decryption key is generated by taking client's identity and server's master secret key as input. Therefore, our encryption scheme can be viewed as an identity-based encryption in Symmetric Key Cryptosystem. Furthermore, the security of the scheme is based on the intractability of factorization search problem over non-abelian algebraic structures. A matrix group over group ring is suggested and an algorithm of computing the inverse of an invertible group ring element is given. Finally, we discuss that our cryptosystem is secure against determinant attacks and quantum attacks.