Provably secure threshold public-key encryption with adaptive security and short ciphertexts

Threshold public-key encryption is a cryptographic primitive allowing decryption control in group-oriented encryption applications. Existing TPKE schemes suffer from long ciphertexts with size linear in the number of authorized users or can only achieve non-adaptive security, which is too weak to capture the capacity of the attackers in the real world. In this paper, we propose an efficient TPKE scheme with constant-size ciphertexts and adaptive security. Security is proven under the decision Bilinear Diffie-Hellman Exponentiation assumption in the standard model. Then we extend our basic construction with efficient trade-offs between the key size and the ciphertext size. Finally, we illustrate improvements to transmit multiple secret session keys in one session with almost no extra cost.