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IEEE photonics journal

(t, n) Threshold Quantum State Sharing Scheme Based on Linear Equations and Unitary Operation

Hao Cao, Wenping Ma

Published Jan 24, 2017• 36 citations
Publisher

Abstract

Quantum state sharing (QSTS) plays an important role in transporting, managing, and distributing keys. In this paper, by adopting the linear equation instead of using the Lagrange interpolation, a new idea of constructing (t, n) threshold quantum state sharing scheme is proposed. The best innovation is that a new tool in constructing (t, n) threshold structure is proposed. In this scheme, the dealer who possesses a sequence of one-particle unknown quantum states intends to share it with n participants and authorizes t out of them cooperate to reconstruct the sequence. First, the equations decided by the private key of dealer are constructed. Second, the dealer distributes the private keys of n participants by using the solutions to the equations just mentioned. Finally, the dealer encodes the sequence through a unitary operation, and any t out of the n participants recover the initial quantum state sequence through the unitary operations decided by the solutions to the linear equations. Compared to the existing schemes, the proposed scheme is easily realized in physical experiment, and its successful probability is 100% theoretically.

DOI
10.1109/jphot.2017.2657232

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Quantum state sharing (QSTS) plays an important role in transporting, managing, and distributing keys. In this paper, by adopting the linear equation instead of using the Lagrange interpolation, a new idea of constructing (t, n) threshold quantum state sharing scheme is proposed. The best innovation is that a new tool in constructing (t, n) threshold structure is proposed. In this scheme, the dealer who possesses a sequence of one-particle unknown quantum states intends to share it with n participants and authorizes t out of them cooperate to reconstruct the sequence. First, the equations decided by the private key of dealer are constructed. Second, the dealer distributes the private keys of n participants by using the solutions to the equations just mentioned. Finally, the dealer encodes the sequence through a unitary operation, and any t out of the n participants recover the initial quantum state sequence through the unitary operations decided by the solutions to the linear equations. Compared to the existing schemes, the proposed scheme is easily realized in physical experiment, and its successful probability is 100% theoretically.
Quantum state sharing (QSTS) is a hot topic in quantum cryptography. However, majority of the current structures cannot resist the participant's fraud well during the initial state reconstruction phase. Especially, verifiable QSTS scheme which can be used to share unknown quantum state has yet to emerge. In this paper, we will propose the first verifiable structure by improving an existing threshold QSTS scheme. Our scheme has three merits: 1) it is easily realized in physical experiment because only the simple oneparticle unitary operations were involved; 2) each dishonest behavior of one participant could be detected by the next client; and 3) the private key of the dealer could be reused for many times.
Abstract The ( t , n ) -threshold schemes offer significant advantages over n , n -threshold schemes due to their flexibility, fault tolerance, and practicality. In this paper, a ( t , n ) -threshold quantum secret-sharing (QSS) and quantum state sharing schemes based on single photons are proposed by incorporating unitary phase shift operations. The proposed scheme employs symmetric bivariate polynomials and utilizes polynomial interpolation for secret sharing. This approach facilitates the secure distribution of classical data and quantum states while maintaining confidentiality and integrity during transmission. Mutual identity authentication between the dealer and participants is ensured, and the accuracy of secret reconstruction is achieved using Lagrange interpolation. The analysis demonstrates that the proposed scheme is resilient against common interception methods, including eavesdropping attacks and participant-driven threats such as entanglement swapping. Additionally, the scheme is characterized by ease of implementation within physical frameworks and adaptability to various applications offering a practical and efficient alternative to existing methods.
Abstract Threshold quantum secret sharing is a typical method for quantum secret sharing (QSS) schemes. In this paper, we propose a verifiable t , n threshold QSS scheme based on the d -dimensional Bell state and asymmetric binary polynomial. In this scheme, the dealer encodes the secret using the asymmetric binary polynomial and generates the corresponding secret share for each participant. Then, the dealer prepares the d -dimensional Bell state, and the participants perform corresponding unitary operations on the particles in transmission to recover the secret. With the hash function and the session key pairs, not only the cheating behavior of the dishonest participants can be detected, but also the specific cheaters can be identified. Furthermore, we consider the case when no less than t participants cooperate to recover the secret, which makes the proposed scheme more practical. Analyses show that the scheme can resist forgery attack, collusion attack and other common attacks.
Abstract With the rapid development of quantum computing, traditional encryption methods face growing security threats. Quantum Secret Sharing (QSS) has emerged as a promising solution, using quantum principles to improve communication security and prevent internal and external attacks. This study proposes a new (t, n) Threshold Quantum Secret Sharing (TQSS) protocol based on single-qubit unitary operations and Lagrange interpolation. The protocol allows secret reconstruction without third-party or dealer assistance and remains efficient even when some participants are absent. To address more complex real-world scenarios, we extend our previously proposed (t, n) TQSS protocol into a Conditional Dynamic TQSS (CDTQSS). This approach uses resource-based share splitting to allow new participants to join without requiring the dealer to redistribute information. However, the protocol is ‘conditional’ because existing participants must take on extra responsibility-they must assist in generating shares for new members and also participate in the secret reconstruction process together with them. The protocol maintains strong security, reduces resource consumption, and offers better flexibility, making it well-suited for practical and dynamic quantum communication needs.
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.
Quantum secret sharing is an important branch of quantum cryptography, and secure multi-party quantum key distribution protocols can be constructed using quantum secret sharing. In this paper, we construct a quantum secret sharing scheme built on a constrained (t, n ) threshold access structure, where n is the number of participants and t is the threshold number of participants and the distributor. Participants from two different sets perform the corresponding phase shift operations on two particles in the GHZ state passed to them, and then t−1 participants with the distributor can recover the key, where the participant recovering the key measures the particles received by himself and finally obtains the key through the collaboration of the distributors. Security analysis shows that this protocol can be resistant to direct measurement attacks, interception retransmission attacks, and entanglement measurement attacks. This protocol is more secure, flexible, and efficient compared with similar existing protocols, which can save more quantum resources.