Abstract Based on the d-dimensional Greenberger–Horne–Zeilinger (GHZ) state, this paper proposes a novel multi-party quantum secret sharing scheme with the characteristics of identity authentication and dual-threshold. In the scheme, the dealer first constructs an asymmetric binary polynomial and decomposes it into two unary polynomials, then divides the participants into two groups, and generates secret shares and corresponding polynomial pairs for each participant. The dealer prepares a three-qudit GHZ state and uses two of them to perform dual-line transmission between the two groups of participants. The participants perform specific unitary transformations on the transmitted particles. Finally, the recovery agent collects and measures the information particles to recover the secret. The scheme uses a hash function and a session key to detect fraudulent behavior and identify specific participants to achieve identity authentication. Security analysis shows that the scheme can effectively resist intercept-resend attacks, entangle-measure attacks, dishonest participant attacks and Trojan horse attacks.
Abstract Based on the d-dimensional Greenberger–Horne–Zeilinger (GHZ) state, this paper proposes a novel multi-party quantum secret sharing scheme with the characteristics of identity authentication and dual-threshold. In the scheme, the dealer first constructs an asymmetric binary polynomial and decomposes it into two unary polynomials, then divides the participants into two groups, and generates secret shares and corresponding polynomial pairs for each participant. The dealer prepares a three-qudit GHZ state and uses two of them to perform dual-line transmission between the two groups of participants. The participants perform specific unitary transformations on the transmitted particles. Finally, the recovery agent collects and measures the information particles to recover the secret. The scheme uses a hash function and a session key to detect fraudulent behavior and identify specific participants to achieve identity authentication. Security analysis shows that the scheme can effectively resist intercept-resend attacks, entangle-measure attacks, dishonest participant attacks and Trojan horse 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.
In this paper, we propose an efficient multi-party quantum secret sharing scheme based on GHZ entangled state. The participants in this scheme are divided into two groups, and share secrets as a group. There is no need to exchange any measurement information between the two groups, reducing the security problems caused by the communication process. Each participant holds one particle from each GHZ state; it can be found that the particles of each GHZ state are related after measuring them, and the eavesdropping detection can detect external attacks based on this characteristic. Furthermore, since the participants within the two groups encode the measured particles, they can recover the same secrets. Security analysis shows that the protocol can resist the intercept-and-resend attack and entanglement measurement attack, and the simulation results show that the probability of an external attacker being detected is proportional to the amount of information he can obtain. Compared with the existing protocols, this proposed protocol is more secure, has less quantum resources and is more practical.
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.
Abstract Quantum secret sharing plays a key role as a foundational method for disseminating a secret to all participants in quantum cryptography. Group authentication plays a significant role in safeguarding information, as it confirms the identity of communication parties. This paper presents a d−level (t,m) threshold quantum secret-sharing scheme combined with group authentication. Group members can simultaneously authenticate their identities through group authentication. Leveraging the Lagrange interpolation polynomial, the group authentication method disperses multiple secret shares to group members and later allows joint verification of some or all members. According to our analysis, the complexities of our group authentication scheme are much lower than those found in widely recognized existing group authentication methods. This algorithm allows each participant to keep their secret shares secure and undisclosed. By avoiding transmission of these shares, external eavesdroppers are unable to obtain any secret information. This protocol offers security, efficiency, and practicality. Security analysis reveals its ability to resist intercept-resend attacks, entangle-measure attacks, collusion attacks, and forgery attacks. The proposed scheme ensures both confidentiality and integrity.
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 Numerous high-quality quantum secret sharing (QSS) protocols have been proposed as integral components of quantum cryptography. However, only a limited number effectively integrate both dynamic and verifiable characteristics. This paper proposes a verifiable dynamic (t, n) QSS protocol based on the asymmetric binary polynomial and the d-dimensional Bell states. In the protocol, the dealer can find out the internal fraudsters by verifying whether an agent has used a correct share. The agents can also verify the correctness of the shares provided by the dealer. Besides, the dealer has the capability to independently adding or revoking of agents without requiring assistance from other agents. Furthermore, the protocol requires at least t agents to recover the secret, which makes the proposed protocol more flexible and practical than existing protocols. Our protocol shows good robustness against the intercept-and-resend, the entangle-and-measure, the internal, and the dishonest revoked agent attacks.