Abstract Quantum secret sharing occupies an important position in quantum cryptography. In this paper, we propose two ( w , ω , n ) weighted threshold quantum secret sharing schemes on d-level single quantum systems that share classical information and quantum states, respectively. The dealer Alice distributes the secret share to each participant using the Chinese Remainder Theorem(CRT) for a polynomial ring, which can realize secret sharing among participants with different weights. In classical information sharing, the dealer can share multiple secrets in one round of the protocol and the participants can verify the correctness of the recovered secrets. In quantum state sharing, the dealer can share multiple single quantum states in one round of protocol. Finally, we demonstrate that our scheme is resistant to common external and internal attacks and compare it with related schemes.
Abstract Quantum secret sharing occupies an important position in quantum cryptography. In this paper, we propose two ( w , ω , n ) weighted threshold quantum secret sharing schemes on d-level single quantum systems that share classical information and quantum states, respectively. The dealer Alice distributes the secret share to each participant using the Chinese Remainder Theorem(CRT) for a polynomial ring, which can realize secret sharing among participants with different weights. In classical information sharing, the dealer can share multiple secrets in one round of the protocol and the participants can verify the correctness of the recovered secrets. In quantum state sharing, the dealer can share multiple single quantum states in one round of protocol. Finally, we demonstrate that our scheme is resistant to common external and internal attacks and compare it with related schemes.
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 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 holds a significant place in quantum cryptography. In this paper, a (w, t, n)-weighted threshold dynamic quantum secret sharing scheme with cheating identification is constructed based on the CRT for a polynomial ring. In our scheme, on the premise of not altering the private shares of the old participants, the dynamic update of the participants can be realized without other participants’ help, and the shared secret will not be changed. During the secret reconstruction phase, via executing the quantum state digital signature, the proposed scheme not only can timely detect the existence of the cheating behavior, but also once exists, definitely can identify one cheater and eliminate him from the system, making the scheme more secure. Moreover, our scheme enables secret sharing among participants with different authorities, which enhances the practicability of the scheme. Finally, the security analysis shows our scheme not only is resistant to a range of typical external attacks but can detect forgery, collusion, denial and dishonest revoked participant attacks.
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.
(t, n) Threshold Quantum Secret Sharing based on a Single d-level Quantum System
A (t, n) threshold quantum secret sharing (QSS) is proposed based on a single d-level quantum system. It enables the (t, n) threshold structure based on Shamir's secret sharing and simply requires sequential communication in the d-level quantum system to recover secret. Besides, the scheme employs an additional qudit to detect cheats and eavesdropping during secret reconstruction, and allows a participant to use the share repeatedly. Analyses show that the proposed scheme is resistant to typical attacks. The scheme is scalable in the number of participants and easier to realize compared to related schemes. More generally, our scheme also presents a generic method to construct new (t, n) threshold QSS schemes based on d-level quantum system with other classical threshold secret sharing.