Secret sharing is a widely-used security protocol and cryptographic primitive in which all people cooperate to restore encrypted information. The characteristics of a quantum field guarantee the security of information; therefore, many researchers are interested in quantum cryptography and quantum secret sharing (QSS) is an important research topic. However, most traditional QSS methods are complex and difficult to implement. In addition, most traditional QSS schemes share classical information, not quantum information which makes them inefficient to transfer and share information. In a weighted threshold QSS method, each participant has each own weight, but assigning weights usually costs multiple quantum states. Quantum state consumption will therefore increase with the weight. It is inefficient and difficult, and therefore not able to successfully build a suitable agreement. The proposed method is the first attempt to build multiparty weighted threshold QSS method using single quantum particles combine with the Chinese remainder theorem (CRT) and phase shift operation. The proposed scheme allows each participant has its own weight and the dealer can encode a quantum state with the phase shift operation. The dividing and recovery characteristics of CRT offer a simple approach to distribute partial keys. The reversibility of phase shift operation can encode and decode the secret. The proposed weighted threshold QSS scheme presents the security analysis of external attacks and internal attacks. Furthermore, the efficiency analysis shows that our method is more efficient, flexible, and simpler to implement than traditional methods.

Scientific ReportsMar 17, 202134 citations

Dynamic and scalable secret sharing schemes based on matrix product compressed states

Hong Lai, Lin‐Chun Wan

Currently, quantum secret sharing (QSS) schemes based on entangled states have not yet fully utilized the potential of the probability amplitude of entangled states. However, the probability amplitude is a key characteristic of quantum information science and possesses significant application prospects in the fields of quantum computing and quantum communication. It is worth noting that entangled states can be effectively represented by matrix product states (MPSs). The representation of entangled states using MPS can precisely reveal the entanglement characteristics closely related to the probability amplitude. This study first focuses on the representation of the W state by using MPS, an approach that allows us to determine the key conditions for W state to achieve quantum advantage in QSS. Subsequently, this research demonstrates that by representing entangled states with MPS, a W state can be compressed into a single photon state and a simplified matrix form, presenting an innovative technical path. Moreover, one of the most attractive features of our proposed QSS scheme is its ability to compress multiple different quantum states (represented by photons) into a unified state represented by a single photon. This characteristic endows our scheme with scalability and flexibility, meaning that the group of participants can be easily expanded or reduced according to their specific needs. The addition of new participants is managed by Alice, who is responsible for the distribution of quantum state shares. On the other hand, when a participant leaves the group, their old quantum state share can be simply ignored in the process of recovering the secret's quantum state, thereby simplifying the management process. Through this strategy, we can not only make effective use of entangled resources but also meet the various requirements of the system, including but not limited to communication security, data transfer rates, and system scalability. This research provides new perspectives and possibilities for the field of quantum information science and may have a significant influence on the development of the field.

Acta Physica SinicaJan 1, 20241 citation