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Scientific Reports

Hybrid threshold adaptable quantum secret sharing scheme with reverse Huffman-Fibonacci-tree coding

Hong Lai, Jun Zhang, Ming‐Xing Luo, Lei Pan, Josef Pieprzyk, Fuyuan Xiao, Mehmet Ali Orgun

Published Aug 12, 2016• 808 citations
Publisher

Abstract

With prevalent attacks in communication, sharing a secret between communicating parties is an ongoing challenge. Moreover, it is important to integrate quantum solutions with classical secret sharing schemes with low computational cost for the real world use. This paper proposes a novel hybrid threshold adaptable quantum secret sharing scheme, using an m-bonacci orbital angular momentum (OAM) pump, Lagrange interpolation polynomials, and reverse Huffman-Fibonacci-tree coding. To be exact, we employ entangled states prepared by m-bonacci sequences to detect eavesdropping. Meanwhile, we encode m-bonacci sequences in Lagrange interpolation polynomials to generate the shares of a secret with reverse Huffman-Fibonacci-tree coding. The advantages of the proposed scheme is that it can detect eavesdropping without joint quantum operations, and permits secret sharing for an arbitrary but no less than threshold-value number of classical participants with much lower bandwidth. Also, in comparison with existing quantum secret sharing schemes, it still works when there are dynamic changes, such as the unavailability of some quantum channel, the arrival of new participants and the departure of participants. Finally, we provide security analysis of the new hybrid quantum secret sharing scheme and discuss its useful features for modern applications.

DOI
10.1038/srep31350

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With prevalent attacks in communication, sharing a secret between communicating parties is an ongoing challenge. Moreover, it is important to integrate quantum solutions with classical secret sharing schemes with low computational cost for the real world use. This paper proposes a novel hybrid threshold adaptable quantum secret sharing scheme, using an m-bonacci orbital angular momentum (OAM) pump, Lagrange interpolation polynomials, and reverse Huffman-Fibonacci-tree coding. To be exact, we employ entangled states prepared by m-bonacci sequences to detect eavesdropping. Meanwhile, we encode m-bonacci sequences in Lagrange interpolation polynomials to generate the shares of a secret with reverse Huffman-Fibonacci-tree coding. The advantages of the proposed scheme is that it can detect eavesdropping without joint quantum operations, and permits secret sharing for an arbitrary but no less than threshold-value number of classical participants with much lower bandwidth. Also, in comparison with existing quantum secret sharing schemes, it still works when there are dynamic changes, such as the unavailability of some quantum channel, the arrival of new participants and the departure of participants. Finally, we provide security analysis of the new hybrid quantum secret sharing scheme and discuss its useful features for modern applications.
Abstract In this paper, we develop a large-capacity quantum digital secret sharing (QDSS) scheme, combined the Fibonacci- and Lucas-valued orbital angular momentum (OAM) entanglement with the recursive Fibonacci and Lucas matrices. To be exact, Alice prepares pairs of photons in the Fibonacci- and Lucas-valued OAM entangled states, and then allocates them to two participants, say, Bob and Charlie, to establish the secret key. Moreover, the available Fibonacci and Lucas values from the matching entangled states are used as the seed for generating the Fibonacci and Lucas matrices. This is achieved because the entries of the Fibonacci and Lucas matrices are recursive. The secret key can only be obtained jointly by Bob and Charlie, who can further recover the secret. Its security is based on the facts that nonorthogonal states are indistinguishable, and Bob or Charlie detects a Fibonacci number, there is still a twofold uncertainty for Charlie' (Bob') detected value.
Abstract In this paper, we show that a (2, 3) discrete variable threshold quantum secret sharing scheme of secure direct communication can be achieved based on recurrence using the same devices as in BB84. The scheme is devised by first placing the shares of smaller secret pieces into the shares of the largest secret piece, converting the shares of the largest secret piece into corresponding quantum state sequences, inserting nonorthogonal state particles into the quantum state sequences with the purpose of detecting eavesdropping, and finally sending the new quantum state sequences to the three participants respectively. Consequently, every particle can on average carry up to 1.5-bit messages due to the use of recurrence. The control codes are randomly prepared using the way to generate fountain codes with pre-shared source codes between Alice and Bob, making three participants can detect eavesdropping by themselves without sending classical messages to Alice. Due to the flexible encoding, our scheme is also dynamic, which means that it allows the participants to join and leave freely.
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 Since the use of a quantum channel is very expensive for transmitting large messages, it is vital to develop an effective quantum compression encoding scheme that is easy to implement. Given that, with the single-photon spin-orbit entanglement, we propose a quantum secret sharing scheme using orbital angular momentum onto multiple spin states based on Fibonacci compression encoding. In our proposed scheme, we can represent the frequency of any secret message which is typically collection of bits encodings of text or integers as a bitstring using the base Fibonacci sequence, which is encoded multiple spin states for secret shares transmitted to participants. We demonstrate that Fibonacci compression encoding carries excellent properties that enable us to achieve more robust quantum secret sharing schemes with fewer number of photons.
Quantum secret sharing is a fundamental technique in quantum cryptography. However, in practical quantum networks, it still faces several bottlenecks, such as high quantum communication cost and low transmission efficiency. To reduce the communication cost, ramp quantum secret sharing schemes have been proposed in existing studies. Nevertheless, intermediate sets in such schemes may leak partial information about the secret. To address this problem, this paper presents a method for detecting intermediate sets. Based on this method, we further propose a communication-efficient perfect quantum secret sharing scheme with eavesdropping detection capability.We analyze the communication cost under different numbers of participating parties and determine the range of participants that minimizes the reconstruction communication cost. The results verify the communication efficiency and security of the proposed scheme.
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.