Secret sharing is a key technology of data confidentiality, where one can distribute a secret among agents, and only the authorized agents can recover the original secret. Quantum information technology, including quantum communication, quantum computing can break through the bottlenecks of classical technology in information security and computing speed, based on quantum mechanics, such as quantum superposition, quantum uncertainty, quantum no-cloning and quantum entanglement. By combining quantum technology with classic secret sharing, the concept of quantum state sharing was presented. In this manuscript, a novel kind of (n,t) threshold quantum state sharing scheme is proposed, where the selected t agents among n agents can cooperate to reconstruct the target secret state. For implementing this scheme, the Chinese reminder theorem is introduced during the processing of the secret key distribution. In addition, to show the proposed scheme clearly, a concrete (5,3) example is given. Furthermore, the proof of the correctness of the scheme is shown. Our scheme will improve the development the quantum secret sharing and open up exploring the application of quantum information technology
Secret sharing is a key technology of data confidentiality, where one can distribute a secret among agents, and only the authorized agents can recover the original secret. Quantum information technology, including quantum communication, quantum computing can break through the bottlenecks of classical technology in information security and computing speed, based on quantum mechanics, such as quantum superposition, quantum uncertainty, quantum no-cloning and quantum entanglement. By combining quantum technology with classic secret sharing, the concept of quantum state sharing was presented. In this manuscript, a novel kind of (n,t) threshold quantum state sharing scheme is proposed, where the selected t agents among n agents can cooperate to reconstruct the target secret state. For implementing this scheme, the Chinese reminder theorem is introduced during the processing of the secret key distribution. In addition, to show the proposed scheme clearly, a concrete (5,3) example is given. Furthermore, the proof of the correctness of the scheme is shown. Our scheme will improve the development the quantum secret sharing and open up exploring the application of quantum information technology
Abstract Threshold quantum secret sharing is a cryptography technique for dividing and reconstructing secret information. The dealer shares a secret based on quantum mechanics principles, and a subset of participants cooperate to recover that secret. For example, in k , n quantum threshold scheme and n , n quantum threshold scheme, the former can only reconstruct the secret when at least k shares are collected. The latter requires all n shares to be collected to reconstruct the secret. However, in real scenarios, the priority of participant identities may vary. In order to meet the actual needs of participants with different rights, this paper proposes a w , ω , n quantum secret sharing (QSS) scheme. When the sum of participants’ weights w is greater than or equal to a threshold ω, they can cooperate to reconstruct the secret. In order to achieve this, this paper uses the entangled state of single particles and constructs a verifiable QSS scheme based on the Chinese remainder theorem. Significantly, in case of a dishonest participant, the dealer can delete the participant before recovering the secret to ensure the security of the communication. This scheme is more flexible than other threshold protocols. At the same time, it reduces the communication cost of the participants. In addition, security analysis shows that the scheme resists typical external and internal attacks.
Threshold quantum secret sharing schemes are incredibly complex systems, making even constructed schemes so complicated as to be very difficult to implement. In addition, most of these schemes share classical information rather than true quantum information. Weighted threshold quantum secret sharing schemes are especially complex, so much so that, to date, no one has been able to successfully construct one. In light of this, this study uses the Chinese Remainder Theorem and performs the phase shift operation on a quantum state to build a weighted threshold secret sharing scheme. The proposed scheme allocates each participant in the scheme their own weight. The dealer then selects a key and encodes it on a secret of quantum state with the phase shift operation. One this is achieved, the dealer divides the key into partial keys, and sends them to the participants. When the sum of the weights of participants is greater than or equal to a fixed threshold, the participants can reconstruct the secret and obtain the quantum information. The proposed scheme is an efficient and flexible weighted threshold quantum secret sharing and is simpler and easier to implement than earlier ones.
Secret sharing of a quantum state, or quantum secret sharing, in which a dealer wants to share certain amount of quantum information with a few players, has wide applications in quantum information.The critical criterion in a threshold secret sharing scheme is confidentiality; with less than the designated number of players, no information can be recovered.Furthermore, in a quantum scenario, one additional critical criterion exists; the capability of sharing entangled and unknown quantum information.Here by employing a six-photon entangled state, we demonstrate a quantum threshold scheme, where the shared quantum secrecy can be efficiently reconstructed with a state fidelity as high as 93%.By observing that any one or two parties cannot recover the secrecy, we show that our scheme meets the confidentiality criterion.Meanwhile, we also demonstrate that entangled quantum information can be shared and recovered via our setting, which demonstrates that our implemented scheme is fully quantum.Moreover, our experimental setup can be treated as a decoding circuit of the 5-qubit quantum error-correcting code with two erasure errors.
Secret sharing of a quantum state, or quantum secret sharing, in which a dealer wants to share a certain amount of quantum information with a few players, has wide applications in quantum information. The critical criterion in a threshold secret sharing scheme is confidentiality: with less than the designated number of players, no information can be recovered. Furthermore, in a quantum scenario, one additional critical criterion exists: the capability of sharing entangled and unknown quantum information. Here, by employing a six-photon entangled state, we demonstrate a quantum threshold scheme, where the shared quantum secrecy can be efficiently reconstructed with a state fidelity as high as 93%. By observing that any one or two parties cannot recover the secrecy, we show that our scheme meets the confidentiality criterion. Meanwhile, we also demonstrate that entangled quantum information can be shared and recovered via our setting, which shows that our implemented scheme is fully quantum. Moreover, our experimental setup can be treated as a decoding circuit of the five-qubit quantum error-correcting code with two erasure errors.
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.
Quantum secret sharing is an important way to achieve secure communications, which has critical applications in the field of information security for its physical properties. According to the perspective of the practical applications, improving the confidentiality and integrity of secret sharing schemes is a good method to increase the security and reliability of communications. In this paper, we propose a quantum secret sharing scheme based on generator matrix segmentation and the structural features of quantum graph states. The security of the secure secret sharing scheme is guaranteed by the pattern of transferring information by stabilizers, scalability of the information and new recovery strategy provided by the entanglement of the related graph states. It puts forward an effective solution to the problem of matrix cycle period, where some numbers without the primitive element cannot construct the generation matrix. First of all, the physical properties of quantum bits (qubits), such as uncertainty principle, no-cloning theorem and indistinguishability, not only optimize the classical schemes but also ensure the absolute safety of communication. Secondly, the application of matrix segmentation makes secret information has better scalability. It improves the coding diversity and the difficulty in deciphering. Thirdly, the favorable entanglement properties and mature experiment preparation techniques of graph states provide an approach to the practical applications. The superiority of the yielded graph states is described in graphical fashion with an elegant stabilizer. Fourthly, the shuffling operation can ensure the independence of the message among participants. Therefore, Eve can not obtain any useful information by measuring randomly. Two group-recovery protocols are proposed to show the secret recovering processing through rebuilding sub-secrets among legal cooperative participants. In the scheme design, the dealer extracts the classical secret information according to the corresponding principle between the classical and quantum information, and divides the classical secret through generated matrix which is produced with the primitive elements in finite domain satisfying the linear independence for any k column vectors. Then the dealer encodes information into graph states and distributes particles to the legal participants with unitary operations. Subsequently, the credible center obtains sub-secrets by the theory of graph states and the group recovery protocol. He can achieve the initial classical secret via the inverse algorithm of matrix segmentation. After getting the classical secret, he recovers quantum secret according to the relationship between classical information and quantum information. Theoretical analysis shows that this scheme can provide better security and scalability of the information. It is appropriate to realize the secret sharing in the quantum network communication to protect secrets from eavesdropping. Also, it can provide an approach to designing diverse and scalable quantum secure communication schemes based on quantum graph states, the algorithm of matrix segmentation, and group-recovery protocol.