We construct general schemes for multipartite quantum secret sharing using multilevel systems, and find that the consistency conditions for valid measurements can be summarized in two simple algebraic conditions. The scheme using very high-dimensional mutually unbiased bases can in principle achieve perfect security against intercept-resend attack; and for the scheme using mutually biased bases, it reaches the optimal but nonperfect security at the four-level system. We also address the security issue against general attacks in the context of our multilevel schemes. In particular, we propose a protocol to enhance both the efficiency and the security against an entanglement-assisted participant's attack by incorporating quantum-key-distribution and measurement-basis-encrypted schemes so that its security is as robust as quantum-key distribution.
We construct general schemes for multipartite quantum secret sharing using multilevel systems, and find that the consistency conditions for valid measurements can be summarized in two simple algebraic conditions. The scheme using very high-dimensional mutually unbiased bases can in principle achieve perfect security against intercept-resend attack; and for the scheme using mutually biased bases, it reaches the optimal but nonperfect security at the four-level system. We also address the security issue against general attacks in the context of our multilevel schemes. In particular, we propose a protocol to enhance both the efficiency and the security against an entanglement-assisted participant's attack by incorporating quantum-key-distribution and measurement-basis-encrypted schemes so that its security is as robust as quantum-key distribution.
Abstract Quantum secret sharing, a pivotal research domain within quantum cryptography, has significant applications across diverse fields such as information security and distributed quantum computing. This paper proposes a d-dimensional hierarchical quantum multi-secret sharing scheme with a general access structure. In the proposed scheme, the distributor constructs a special entangled state by leveraging the secret values at each level and a monotone span program. During the secret reconstruction phase, participants only need to measure the particles in their possession, and authorized participants at each level can recover multiple secrets shared at that level. Additionally, each participant can independently compute and obtain multiple lower-level secrets but cannot access any higher-level secret information. Compared to existing hierarchical quantum secret sharing schemes, the proposed scheme is better suited for specific application scenarios with unique requirements. Furthermore, security analysis demonstrates that the scheme can resist various attacks, such as measurement attacks, intercept-resend attacks, entanglement-measurement attacks, Trojan horse attacks, and collusion attacks.
The aim of quantum secret sharing, as one of most promising components of quantum cryptograph, is one-to-multiparty secret communication based on the principles of quantum mechanics. In this paper, an efficient multiparty quantum secret sharing protocol in a high-dimensional quantum system using a single qudit is proposed. Each participant's shadow is encoded on a single qudit via a measuring basis encryption method, which avoids the waste of qudits caused by basis reconciliation. Security analysis indicates that the proposed protocol is immune to general attacks, such as the measure-resend attack, entangle-and-measure attack and Trojan horse attack. Compared to former protocols, the proposed protocol only needs to perform the single-qudit measurement operation, and can share the predetermined dits instead of random bits or dits.
In this paper, we give the mutually unbiased bases on the p^2 -dimensional quantum system where p is an odd prime number, and construct the corresponding unitary transformation based on the properties of these mutually unbiased bases. Then, we construct a (N,N) threshold secret sharing scheme using unitary transformation between these mutually unbiased bases, and analyze the scheme's security by several ways, for example, intercept-and-resend attack, entangle-and-measure attack, Trojan horse attack, and so on. Using our method, we construct a single-particle quantum protocol involving only one qudit, and the method shows much more scalability than other schemes.
We investigate the security bounds of quantum-cryptographic protocols using d-level systems. In particular, we focus on schemes that use two mutually unbiased bases, thus extending the Bennett-Brassard 1984 quantum-key-distribution scheme to higher dimensions. Under the assumption of general coherent attacks, we derive an analytic expression for the ultimate upper security bound of such quantum-cryptography schemes. This bound is well below the predictions of optimal cloning machines. The possibility of extraction of a secret key beyond entanglement distillation is discussed. In the case of qutrits we argue that any eavesdropping strategy is equivalent to a symmetric one. For higher dimensions such an equivalence is generally no longer valid.
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.
We present a detailed security analysis of a d -dimensional quantum key distribution protocol based on two and three mutually unbiased bases (MUBs) both in an asymptotic and finite-key-length scenario. The finite secret key rates (in bits per detected photon) are calculated as a function of the length of the sifted key by (i) generalizing the uncertainly relation-based insight from BB84 to any d -level 2-MUB QKD protocol and (ii) by adopting recent advances in the second-order asymptotics for finite block length quantum coding (for both d -level 2- and 3-MUB QKD protocols). Since the finite and asymptotic secret key rates increase with d and the number of MUBs (together with the tolerable threshold) such QKD schemes could in principle offer an important advantage over BB84. We discuss the possibility of an experimental realization of the 3-MUB QKD protocol with the orbital angular momentum degrees of freedom of photons.