Efficient sharing of many secrets

Ding Xing, Yifei Wang, Zhao Dou +3 more

Semi-quantum secret sharing (SQSS) is a branch of quantum cryptography which only requires the dealer to have quantum capabilities, reducing the difficulty of protocol implementation. However, the efficiency of the SQSS protocol still needs to be further studied. In this paper, we propose a semi-quantum secret sharing protocol, whose efficiency can approach 100% as the length of message increases. The protocol is based on single particles to reduce the difficulty of resource preparation. Particle reordering, a simple but effective operation, is used in the protocol to improve efficiency and ensure security. Furthermore, our protocol can share specific secrets while most SQSS protocols could not. We also prove that the protocol is secure against common attacks.

Wen‐Ai Jackson, Keith M. Martin, Christine M. O’Keefe

Pradeep Kiran Sarvepalli, Robert Raussendorf

A secret-sharing scheme is a cryptographic protocol to distribute a secret state in an encoded form among a group of players such that only authorized subsets of the players can reconstruct the secret. Classically, efficient secret-sharing schemes have been shown to be induced by matroids. Furthermore, access structures of such schemes can be characterized by an excluded minor relation. No such relations are known for quantum secret-sharing schemes. In this paper we take the first steps toward a matroidal characterization of quantum-secret-sharing schemes. In addition to providing a new perspective on quantum-secret-sharing schemes, this characterization has important benefits. While previous work has shown how to construct quantum-secret-sharing schemes for general access structures, these schemes are not claimed to be efficient. In this context the present results prove to be useful; they enable us to construct efficient quantum-secret-sharing schemes for many general access structures. More precisely, we show that an identically self-dual matroid that is representable over a finite field induces a pure-state quantum-secret-sharing scheme with information rate $1$.

Carlo Blundo, Alfredo De Santis, Giovanni Di Crescenzo +2 more

Prabhanjan Ananth, Vipul Goyal, Jiahui Liu +1 more

Feixiang Li, Tingyan Chen, Meng Li +1 more

Quantum secret sharing plays a crucial role in quantum cryptography. The two main trends in quantum secret sharing are to address the problem of scheme failure due to participant spoofing and to improve the efficiency of quantum secret sharing. This paper focuses on the quantum secret sharing scheme with general access structure due to its flexibility. We design a special entangled state by resorting to Monotone Span Program (MSP). Based on the special 2-dimensional entangled state, an efficient and verifiable general quantum secret sharing (GQSS) scheme is proposed. In the GQSS scheme, the authorized participants only provide the X-basis measurement results of particles to recover and verify the shared secret, which makes that our scheme have lower communication consumption and quantum computational complexity. The analysis shows that the proposed scheme is simpler and more practical compared with related quantum secret sharing schemes.