A Secure Threshold Signature Scheme from Lattices

Lattices are the most fascinating mathematical tool used in modern cryptography. Cryptographic schemes based on lattices have got rapid development in almost all areas, like public key encryption, group and ring signature, identity-based encryption, attribute-based encryption, and even fully homomorphic encryption, except that there barely are not threshold schemes. In this work, we give a direct construction of a threshold signature scheme from lattices, which is proved to be non-adaptive existential unforgeable in the random oracles. Our scheme do not need any interactions between the players. The dealer holds the system public key. Each player holds its own public-secret pair. Each player gets verified signature share separately and combines all individual signature shares into a final signature. Furthermore, the dealer can not imitate the signature shares.