An efficient lattice-based threshold signature scheme using multi-stage secret sharing

Secret sharing is a cryptographic technique used in many different applications such as cloud computing, multi-party computation and electronic voting. Security concerns in these applications are data privacy, availability, integrity and verifiability, where secret sharing provides proper solutions. The authors address some important features like verifiability and being multi-stage to make it usable in various field of application. Here, the authors propose an anonymous threshold signature scheme based on the trapdoor function introduced by Micciancio and Peikert by sharing the private key using a lattice-based threshold multi-stage secret sharing (TMSSS) scheme. Then, the authors improve the previously proposed TMSSS scheme, in such a way that less public values are required to publish on the bulletin board which makes the scheme more efficient while preserving the security of the scheme based on the lattice hard problems. The proposed scheme inherits the desired features such as anonymity and verifiability from the improved TMSSS scheme. Furthermore, both schemes use simple matrix operations, which additionally increase the efficiency.