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Quantum Information Processing

Quantum secret sharing with (m, n) threshold: QFT and identity authentication

Priyanka Mawlia, Vikash Siwach, Pankaj Bijaranian, Deepak Singh

Published Oct 16, 2024• 14 citations
Publisher

Abstract

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.

DOI
10.1007/s11128-024-04532-5

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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.
Quantum secret sharing (QSS) is an important branch of quantum cryptography. Identity authentication is a significant means to achieve information protection, which can effectively confirm the identity information of both communication parties. Due to the importance of information security, more and more communications require identity authentication. We propose a d-level (t,n) threshold QSS scheme in which both sides of the communication use mutually unbiased bases for mutual identity authentication. In the secret recovery phase, the sharing of secrets that only the participant holds will not be disclosed or transmitted. Therefore, external eavesdroppers will not get any information about secrets at this phase. This protocol is more secure, effective, and practical. Security analysis shows that this scheme can effectively resist intercept–resend attacks, entangle–measure attacks, collusion attacks, and forgery attacks.
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−d-d−level (t,m)(t, m)(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 The ( t , n ) -threshold schemes offer significant advantages over n , n -threshold schemes due to their flexibility, fault tolerance, and practicality. In this paper, a ( t , n ) -threshold quantum secret-sharing (QSS) and quantum state sharing schemes based on single photons are proposed by incorporating unitary phase shift operations. The proposed scheme employs symmetric bivariate polynomials and utilizes polynomial interpolation for secret sharing. This approach facilitates the secure distribution of classical data and quantum states while maintaining confidentiality and integrity during transmission. Mutual identity authentication between the dealer and participants is ensured, and the accuracy of secret reconstruction is achieved using Lagrange interpolation. The analysis demonstrates that the proposed scheme is resilient against common interception methods, including eavesdropping attacks and participant-driven threats such as entanglement swapping. Additionally, the scheme is characterized by ease of implementation within physical frameworks and adaptability to various applications offering a practical and efficient alternative to existing methods.
Abstract Quantum Secret Sharing (QSS) mitigates critical vulnerabilities in classical cryptographic protocols by leveraging quantum mechanics to achieve information-theoretic security. However, existing QSS schemes encounter challenges related to scalability, resistance to collusive attacks, and the lack of robust participant authentication. This paper proposes a novel ( r , m ) threshold QSS protocol that integrates group authentication with quantum–classical hybrid techniques to address these limitations. By incorporating the Quantum Fourier Transform (QFT), Inverse QFT (IQFT), and controlled-U gate operations within a trivariate polynomial secret-sharing framework, the protocol enhances security against intercept-resend, entangle-measure, and collusive attacks while reducing computational overhead. A practical example is provided to validate the protocol’s effectiveness.
Abstract Quantum secret sharing (QSS) plays a crucial role in quantum cryptography as a privacy preserving scheme. Designing an efficient QSS protocol requires addressing three key challenges: 1) dynamic agent membership (handling agents joining or leaving during execution), 2) adversarial resilience (ensuring robustness against dishonest agents), and 3) practical optimization (improving computational and communication efficiency while minimizing implementation cost). In this paper, a verifiable dynamic threshold QSS (VDQSS) protocol with authentication capability is proposed. The protocol employs single particles for both authentication and share distribution, combining homogeneous linear recursion (HLR) with mutually unbiased bases (MUBs) to reconstruct multiple secrets. This approach significantly enhances security while reducing protocol complexity. The correctness and practicality of the protocol are validated through experimental simulations. Analytical results demonstrate its robustness against common attacks, providing reliable security guarantees for quantum communications. Compared to existing QSS protocols, the protocol offers enhanced simplicity and practical applicability.
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.