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.
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.
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.
A verifiable (t, n) threshold quantum secret sharing scheme with sequential communication was proposed recently. In this work, we analyze its security and then give two new participant attacks. Using the first participant attack, the first participant can obtain the dealer's secrets by himself with nonzero probability without being detected. Using the second participant attack, a dishonest participant can gain access to the dealer's secrets by himself in the secret reconstruction phase while he can make the other participants recover false secrets instead of the real ones without being detected. Furthermore, we present an effective way to prevent these attacks.
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.
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 In the domain of quantum cryptography, the implementation of quantum secret sharing stands as a pivotal element. In this paper, we propose a novel verifiable quantum secret sharing protocol using the d-dimensional product state and Lagrange interpolation techniques. This protocol is initiated by the dealer Alice, who initially prepares a quantum product state, selected from a predefined set of orthogonal product states within the ℂ d ⊗ ℂ d framework. Subsequently, the participants execute unitary operations on this product state to recover the underlying secret. Furthermore, we subject the protocol to a rigorous security analysis, considering both eavesdropping attacks and potential dishonesty from the participants. Finally, we conduct a comparative analysis of our protocol against existing schemes. Our scheme exhibits economies of scale by exclusively employing quantum product states, thereby realizing significant cost-efficiency advantages. In terms of access structure, we adopt a (t,n)-threshold architecture, a strategic choice that augments the protocol’s practicality and suitability for diverse applications. Furthermore, our protocol includes a rigorous integrity verification mechanism to ensure the honesty and reliability of the participants throughout the execution of the protocol.
A quantum secret sharing (QSS) scheme with single photons was proposed, the trusted third party (TTP) encoded the secret value into conjugate single quantum states, in the revealing phase each participant performs the corresponding unitary operation on the single photon sequence sequentially according to its’ private key, and the participants can recover the secret value only through one round of interaction with the TTP and two round of interactions between themselves, further more any dishonest action and malicious attack can be detected.