Simple and efficient threshold cryptosystem from the Gap Diffie-Hellman group

In this paper, we construct a new threshold cryptosystem from the Gap Diffie-Hellman (GDH) group. The proposed scheme enjoys all the most important properties that a robust and practical threshold cryptosystem should possess, that is, it is noninteractive, computationally efficient and provably secure against adaptive chosen ciphertext attacks. In addition, thanks to the elegant structure of the GDH group, the proposed threshold cryptosystem has shorter decryption shares as well as ciphertexts when compared with other schemes proposed in the literature.