A (
k,n)-threshold secret-sharing scheme allows for a string to be split into
n shares in such a way that any subset of at least
k shares suffices to recover the secret string, but such that any subset of at most $k\ensuremath{-}1$ shares contains no information about the secret. Quantum secret-sharing schemes extend this idea to the sharing of quantum states. Here we propose a method of performing computation securely on quantum shared secrets. We introduce a (
n,n)-quantum secret sharing scheme together with a set of algorithms that allow quantum circuits to be evaluated securely on the shared secret without the need to decode the secret. We consider a multipartite setting, with each participant holding a share of the secret. We show that if there exists at least one honest participant, no group of dishonest participants can recover any information about the shared secret, independent of their deviations from the algorithm.
This article explores the importance and challenges of secret sharing technology in the context of rapid advancements in information technology. With increasing attention on data security and privacy protection, secret sharing serves as a key cryptographic technique that ensures secure data transmission, storage, and multi-party computation by dividing secrets into multiple shares. However, existing solutions encounter performance bottlenecks when dealing with large-scale datasets, managing share updates in dynamic environments, and facing quantum computing threats. This article systematically summarizes the basic concepts, theories, classifications, and characteristics of secret sharing while analyzing its applications in financial security, medical privacy, and other fields. Furthermore, it presents recent research progress on dynamic secret sharing and anti-quantum secret sharing. The findings indicate that dynamic secret sharing schemes improve long-term key storage security, while anti-quantum secret sharing provides a solution to counteract quantum computing threats. This study not only deepens understanding of secret sharing technology but also offers insights for future research directions, significantly contributing to enhancing data protection levels.