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Chinese Physics B

Quantum secret sharing based on quantum error-correcting codes

Zu-Rong Zhang, Wei-Tao Liu, Cheng-Zu Li

Published May 1, 2011• 24 citations
Publisher

Abstract

Quantum secret sharing(QSS) is a procedure of sharing classical information or quantum information by using quantum states. This paper presents how to use a [2 k − 1, 1, k ] quantum error-correcting code (QECC) to implement a quantum ( k , 2 k − 1) threshold scheme. It also takes advantage of classical enhancement of the [2 k − 1, 1, k ] QECC to establish a QSS scheme which can share classical information and quantum information simultaneously. Because information is encoded into QECC, these schemes can prevent intercept-resend attacks and be implemented on some noisy channels.

DOI
10.1088/1674-1056/20/5/050309

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Quantum secret sharing(QSS) is a procedure of sharing classical information or quantum information by using quantum states. This paper presents how to use a [2 k − 1, 1, k ] quantum error-correcting code (QECC) to implement a quantum ( k , 2 k − 1) threshold scheme. It also takes advantage of classical enhancement of the [2 k − 1, 1, k ] QECC to establish a QSS scheme which can share classical information and quantum information simultaneously. Because information is encoded into QECC, these schemes can prevent intercept-resend attacks and be implemented on some noisy channels.
Abstract Quantum secret sharing has wide application prospects in quantum communication, quantum network and other fields. It can provide a secure and reliable information sharing method for multi-party communication. In this paper, we mainly study the connection mechanism between the quantum secret-sharing scheme and quantum error-correcting codes. Firstly, we give the necessary and sufficient conditions for the existence of quantum error-correcting codes based on group algebra theory. Secondly, we give the corresponding quantum secret sharing scheme model with local quantum operation and classical communication capability can be constructed by any given quantum error-correcting codes. The advantage of this model is that the corresponding quantum secret-sharing scheme can be found for any quantum error-correcting code.
The emerging quantum technology has highlighted the necessity for secure and efficient secret sharing in quantum networks. In this paper, we introduce a verifiable multiparty counterfactual quantum secret sharing (QSS) protocol, enhancing security and efficiency. This QSS protocol utilizes a low-depth quantum circuit to encrypt and decrypt information, which comprises a unitary operator constructed using a preshared secret key. To ensure the robustness and verifiability of the shared secret key, the protocol imposes constraints on the participants with the Chinese remainder theorem. The most significant advantage of our proposed QSS protocol is incorporating counterfactual communication, which considerably enhances the scheme’s security by enabling exchange-free information sharing among participants, thereby minimizing the risk of eavesdropping or intercept-and-resend attacks. Furthermore, we incorporate a weighted-threshold mechanism that provides flexibility, enabling diverse use cases to design security protocols for quantum networks. The security analysis of the counterfactual QSS protocol and its implementation on IBM Quantum computers reveals strong resilience to internal and external attacks, along with high efficiency and robustness, making it effective for quantum encryption in the noisy intermediate-scale quantum era.
We present a general scheme for sharing quantum secrets, and an extension to sharing classical secrets, which contain all known quantum-secret-sharing schemes. In this framework, we show the equivalence of existence of both schemes, that is, the existence of a scheme sharing a quantum secret implies that the extended classical-secret-sharing scheme works, and vice versa. As a consequence of this, we find schemes sharing classical secrets for arbitrary access structures. We then clarify the relationship to quantum error correction and observe several restrictions thereby imposed, which for example indicates that for pure-state threshold schemes the share size qqq must scale with the number of players nnn as $q\ensuremath{\ge}\sqrt{n}$. These results also provide a way of searching for quantum-error-correcting codes.
Secret sharing of a quantum state, or quantum secret sharing, in which a dealer wants to share certain amount of quantum information with a few players, has wide applications in quantum information.The critical criterion in a threshold secret sharing scheme is confidentiality; with less than the designated number of players, no information can be recovered.Furthermore, in a quantum scenario, one additional critical criterion exists; the capability of sharing entangled and unknown quantum information.Here by employing a six-photon entangled state, we demonstrate a quantum threshold scheme, where the shared quantum secrecy can be efficiently reconstructed with a state fidelity as high as 93%.By observing that any one or two parties cannot recover the secrecy, we show that our scheme meets the confidentiality criterion.Meanwhile, we also demonstrate that entangled quantum information can be shared and recovered via our setting, which demonstrates that our implemented scheme is fully quantum.Moreover, our experimental setup can be treated as a decoding circuit of the 5-qubit quantum error-correcting code with two erasure errors.
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.