A lattice-based changeable threshold multi-secret sharing scheme and its application to threshold cryptography

Abstract

In this paper, we propose a threshold increasing algorithm for a (t; n) latticebased Threshold Multi-Stage Secret Sharing (TMSSS) scheme. To realize the changeability feature, we use the zero addition protocol to construct a new (t0; n) TMSSS scheme. Therefore, the new scheme enjoys the signi cant feature of threshold changeability along with the inherited features of being multi-stage, multi-use, and veri able derived fromour previously proposed lattice-based TMSSS scheme. Furthermore, we use the improved TMSSS scheme to propose a threshold decryption algorithm for the Learning With Error (LWE) based public key encryption scheme based on the study of Lindner and Peikert. For threshold decryption, each authorized subset of participants decrypts the ciphertext partially and sends the result to the combiner. The combiner can decrypt the ciphertext using the partial decryptions. The security of both schemes is based on hardness of lattice problems, i.e. LWE and Inhomogeneous Small Integer Solution (ISIS) problems, which are believed to resist against the quantum algorithms. The proposed schemes are eficient, especially on the participants' side, making them suitable for the applications in which the participants have limited processing capacities.