Abstract This paper proposed a quantum secret sharing scheme over lattice-based threshold encryption: it integrates resplittable threshold public key encryption (RTPKE) and utilizes a lattice-based private key share transmission mechanism to enhance the security of the share distribution process. By leveraging the dynamic key management features of RTPKE, the scheme can flexibly adjust key distribution as required when participants change. During the quantum secret reconstruction process, the decoy particles do not need to be detected by eavesdroppers when transmitted between participants. Instead, this task is performed by a semi-trusted third party (TP), reducing resource consumption and communication overhead. The decoy particles are not chosen from a fixed quantum bases but are instead in completely random quantum bases, making it impossible for an eavesdropper to obtain the correct result through conventional measurements. The probability of the eavesdropper escaping detection after measuring any decoy particle is nearly zero. After each participant performs a unitary operation, they randomly shuffle the sequence of decoy and information particles. When the particles are transmitted back to the TP, the TP uses the sequence information recorded by the participants to restore the original order and extract the information particles, effectively defending against forgery-replay attacks and potential threats from dishonest participants.
Abstract This paper proposed a quantum secret sharing scheme over lattice-based threshold encryption: it integrates resplittable threshold public key encryption (RTPKE) and utilizes a lattice-based private key share transmission mechanism to enhance the security of the share distribution process. By leveraging the dynamic key management features of RTPKE, the scheme can flexibly adjust key distribution as required when participants change. During the quantum secret reconstruction process, the decoy particles do not need to be detected by eavesdroppers when transmitted between participants. Instead, this task is performed by a semi-trusted third party (TP), reducing resource consumption and communication overhead. The decoy particles are not chosen from a fixed quantum bases but are instead in completely random quantum bases, making it impossible for an eavesdropper to obtain the correct result through conventional measurements. The probability of the eavesdropper escaping detection after measuring any decoy particle is nearly zero. After each participant performs a unitary operation, they randomly shuffle the sequence of decoy and information particles. When the particles are transmitted back to the TP, the TP uses the sequence information recorded by the participants to restore the original order and extract the information particles, effectively defending against forgery-replay attacks and potential threats from dishonest participants.
Threshold public key encryption is a cryptographic primitive where a secret key of an organization is distributed among special members called decryption servers (insiders) and a certain threshold number of insiders must cooperate to decrypt any ciphertext. Threshold public key encryption with an additional randomized algorithm Tsplit is called resplittable threshold public key encryption (RTPKE). Cryptographic primitive RTPKE was introduced by Hanaoka et al. [Generic construction of chosen ciphertext secure proxy re-encryption, in CT-RSA, San Francisco, CA, USA, LNCS, O. Dunkelman, ed., Springer-Verlag, Heidelberg, 2012, pp. 349–364] in a generic construction of chosen ciphertext attack secure proxy re-encryption scheme. In MIST 2013 conference Singh et al. [Lattice based efficient threshold public key encryption scheme, J. Wirel. Mob. Netw. Ubiquitous Comput. Dependable Appl. (JoWUA) 4(4) (2013), pp. 93–107] presented lattice-based RTPKE scheme based on Regev's LWE [On lattices, learning with errors, random linear codes, and cryptography, in STOC, Baltimore, MD, USA, H.N. Gabow and R. Fagin, eds., ACM, University of Wales, Cardiff, 2005, pp. 84–93] assumption. In this paper, we propose lattice-based RTPKE scheme in the identity-based setting.
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.
A verifiable quantum secret sharing protocol using quantum walks on a lattice is proposed in this paper. The protocol utilizes generalized Bell states as the initial quantum resource, integrating the quantum walk evolution operator U with the global shift operator Gab to facilitate joint encrypted transmission among multiple participants. A bidirectional identity authentication mechanism based on hash functions is introduced to ensure the legitimacy of all communication parties, which effectively resists impersonation attacks. Random decoy particles are randomly prepared in either the Zd or Xd basis and inserted into the transmission sequence, enabling real-time eavesdropping detection on the quantum channel. In the secret reconstruction phase, a public verification mechanism is designed to allow participants to verify the correctness of the recovered secret and identify internal dishonest behaviors. Security analysis demonstrates that the protocol achieves information-theoretic security, resisting typical external attacks such as intercept-resend, measure-resend, and entangle-measure attacks, as well as collusion attacks from dishonest internal participants. Compared with existing quantum-walk-based secret sharing schemes, the proposed protocol maintains high qubit efficiency while supporting both identity authentication and public verifiability, thus possessing stronger practicality and security.
Abstract In the field of quantum cryptography, Quantum Secret Sharing (QSS) holds substantial importance, with identity authentication emerging as a key strategy for safeguarding information. It efficiently certifies the identification of both persons involved in the conversation, which contributes to increased security measures. Our proposal, a (m, n) threshold Quantum Secret Sharing (QSS) scheme introduces a unique approach to mutual identity authentication, utilizing mutually unbiased bases. During the secret recovery phase, the scheme ensures that secrets exclusively held by participants remain undisclosed and are not transmitted, reinforcing the security of the communication process. As a result, external eavesdroppers are left empty-handed in their attempt to access information about secrets during this phase. Our protocol surpasses in terms of security, effectiveness, and practicality, proving its resilience against intercept–resend attacks, collusion attacks, collective attacks, and forgery attacks according to a comprehensive security analysis.
Abstract Most of Quantum Secret Sharing(QSS) are (n, n) threshold 2-level schemes, in which the 2-level secret cannot be reconstructed until all n shares are collected. In this paper, we propose a (t, n) threshold d-level QSS scheme, in which the d-level secret can be reconstructed only if at least t shares are collected. Compared with (n, n) threshold 2-level QSS, the proposed QSS provides better universality, flexibility, and practicability. Moreover, in this scheme, any one of the participants does not know the other participants’ shares, even the trusted reconstructor Bob1 is no exception. The transformation of the particles includes some simple operations such as d-level CNOT, Quantum Fourier Transform(QFT), Inverse Quantum Fourier Transform(IQFT), and generalized Pauli operator. The transformed particles need not to be transmitted from one participant to another in the quantum channel. Security analysis shows that the proposed scheme can resist intercept-resend attack, entangle-measure attack, collusion attack, and forgery attack. Performance comparison shows that it has lower computation and communication costs than other similar schemes when 2 < t < n − 1.
Quantum secret sharing (QSS) is a cryptographic protocol that utilizes fundamental principles of quantum mechanics to securely distribute and reconstruct secret information among multiple participants. Most existing protocols rely on entangled states (such as Bell and GHZ states), but in practical applications. The preparation of entangled state is constrained by a short quantum coherence time, low state fidelity, etc., which makes it difficult to implement entangled resource-dependent QSS protocols. In this work, a novel practical and verifiable multi-party QSS protocol is proposed based on orthogonal product states, which are easier to prepare than entangled states. During the protocol preparation stage, the secret distributor first converts pre-shared classical secret information into the corresponding orthogonal product states according to the encoding rules, and pre-shares a communication key with participants via quantum key distribution (QKD), which is used to hide the initial quantum sequence information through subsequent particle transformation operations. After preparing the orthogonal product states, the distributor reorganizes the particles by position, extracting particles at the same position from each state to form new sequences, shuffling their order, then applying Hadamard operations using a pre-shared key, inserting decoy particles, and sending the sequences to the participants. After receiving it, participants conduct eavesdropping detection, use the same key for the inverse transformations, retain one particle from each sequence, and sequentially pass the remaining particles until the last participant receives a complete set, triggering state verification with the arbiter distributor. If the verification is successful, the particles will be returned to the first participant and the return stage will follow the same procedure. Only after both the transmission and return stage verifications have passed, will the distributor reveal the initial particle positions, allowing participants to collaboratively reconstruct the secret. In the protocol, the secret distributor acts as an arbitrator to verify the particle state information together with participants at designated points (the end of the transmission stage and the end of the return stage) in order to determine whether the particle-state information is error-free during transmission. If the verification fails at either stage, the protocol will be terminated immediately. Meanwhile, considering that the number of participants may change during the execution of the protocol, a dynamic scheme for personnel changes is designed to ensure the flexibility of the protocol. Through the analysis of possible internal and external attacks, It can be proven that our protocol can effectively resist the existing common attack. Using Qiskit simulation experiments, the core quantum procedures of the protocol can be successfully modeled. The experimental results provide strong computational validation of the theoretical feasibility of the protocol.