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arXiv:1801.05939

A secret sharing scheme on p^2 -dimensional quantum system

Na Hao, Zhihui Li, Bai, Hai-Yan, Chen‐Ming Bai

Published Jan 18, 2018• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.1801.05939

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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.
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.
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 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 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.
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.
(ttt, nnn) Threshold Quantum Secret Sharing based on a Single ddd-level Quantum System
A (ttt, nnn) threshold quantum secret sharing (QSS) is proposed based on a single ddd-level quantum system. It enables the (ttt, nnn) threshold structure based on Shamir's secret sharing and simply requires sequential communication in the ddd-level quantum system to recover secret. Besides, the scheme employs an additional qudit to detect cheats and eavesdropping during secret reconstruction, and allows a participant to use the share repeatedly. Analyses show that the proposed scheme is resistant to typical attacks. The scheme is scalable in the number of participants and easier to realize compared to related schemes. More generally, our scheme also presents a generic method to construct new (ttt, nnn) threshold QSS schemes based on ddd-level quantum system with other classical threshold secret sharing.