Two Identity Based Threshold Cryptosystem with Reduced Trust in PKG

In the traditional identity based cryptosystems, since private key generator (PKG) is able to compute the private key corresponding to any identity, the malicious activities of PKG would be hard to find, which restricts the use of identity based cryptosystems. People have employed multiple PKGs to solve this problem. However it brings other problems. In this paper, two identity based threshold cryptosystems are proposed, which reduce the trust in PKG. The traceable identity based encryption technique suggested by Goyal is used, which successfully restricts the potential misbehaviors of PKG, and the idea of public verifiable encryption which is widely used in the threshold cryptosystems to achieve distributed decryption. These two schemes solve the malicious PKG tracing problem effectively, and if PKG generates more than one private key to a single user, the misbehavior could be detected with evidence. We define the formal model of identity based threshold cryptosystem with reduced trust in PKG. We also prove the two schemes' security against the adaptive chosen ciphertext attack, the find key attack and the compute new key attack under the formal security model. The result shows that their security is based on the truncated augmented bilinear Diffie-Hellman exponent assumption.