Quantum walk based quantum secret sharing in a verifiable framework

Secret sharing is a cryptographic primitive which plays a central role in various tasks including secure multi-party computation and key management. Quantum schemes for secret sharing commonly rely on multi-particle entangled quantum states, which remains challenging with current experimental technologies. Firstly, in this paper we present a (t,n) quantum secret sharing scheme based on quantum walks on a circle, which only involves two-particle product states as the initial quantum resource. When recovering the secrets, it requires at least t participants sequentially completing their operations on the communicated state, while less than t participants can not acquire any information about the secrets. Secondly, a verification mechanism is designed, which can detect cheats with an asymptotic probability 100%. Finally, we show that the scheme is perfectly correct and is secure against common attacks including collusion attack. In conclusion, the proposed scheme will be useful for quantum communication networks due to its inherent scalability, flexibility and information-theoretical security.