Quantum multi-secret sharing via trap codes and discrete quantum walks

In this paper, we propose a fully quantum multi-secret sharing scheme. In contrast with regular secret sharing schemes, multi-secret sharing schemes share a set of unknown secrets, and during the reconstruction phase, all the secrets are reconstructed. The main technique is to suitably modify a quantum trap code to construct a scheme where increasing number of secret states are recovered as more and more participants combine their shares. It is desirable that the dimensions of the share states are within implementable limits. In view of this and due to the significantly large dimension of the share states produced by our first construction, we introduce a discrete-time quantum walk-based technique to reduce the dimension of the shares making the schemes more suitable for practical purposes. Our methods are unconditional and do not depend on any computational hardness assumptions like lattice-based problems. Our scheme is simple, secure against adversarial attacks and can be easily modified into several variants of multi-secret sharing schemes.