Cheating immune multi-secret sharing without predefined order of secrets
Changlu Lin, Xingfu Yan, Qiwen Niu, Huidan Hu · Journal of the Chinese Institute of Engineers · 2019
A (t,n)-threshold secret sharing scheme divides a secret into n pieces and distributes them to n players privately, in such a way that any t or more players who collect their pieces can reconstruct the secret correctly, while any t−1 players know no information about the secret. To improve efficiency, a multi-secret sharing scheme is proposed in which multiple secrets are shared at one time. In this paper, we propose a new multi-secret sharing scheme based on hash function. We combine the mathematical ‘shift values’ proposed by He and Dawson in 1994 with asymmetric bivariate polynomials to construct pseudo shares. Our scheme has the following three extended properties: cheaters are detected thanks to the hash function, each share is used many times in secret reconstruction, and the order of recovery of secrets is not predefined. Furthermore, a secure channel between dealer and players is unnecessary, unlike some existing multi-secret sharing schemes.