Selectively chosen ciphertext security in threshold public-key encryption

Threshold public-key encryption can control decryption abilities of an authorized user group in such a way that each user of the group can produce only a decryption share and at least t of them should collect decryption shares to recover a message. We present a new threshold public-key encryption that is secure against selectively chosen ciphertext attacks. Semantic security against chosen ciphertext adversaries is the de facto level of security for public-key encryption deployed in practice because many encryption systems are broken in a model of chosen ciphertext security. The security of the proposed system is formally proved without random oracles under a new assumption. We also provide proof of the intractability of our assumption in the generic group model.