Abstract
Chai, Cao and Lu first proposed an ID-based threshold decryption scheme without random oracles. Their approach is based on the Bilinear Diffie-Hellman Inversion assumption, and prove that it is selective chosen plaintext secure without random oracles. However, to ensure correctness of their ID-based threshold decryption scheme, it is necessary to guarantee that the shared decryption is performed correctly through some public verification function. We modify Chai et al.’s scheme to ensure that all decryption shares are consistent. We also present the first mediated ID based encryption scheme based on the Bilinear Diffie Hellman Inversion assumption without random oracles. In addition, we extend it into a mediated hierarchical ID-based encryption scheme.
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