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arXiv:1801.09500 · Physical Review A

Communication efficient quantum secret sharing

Kaushik Senthoor, Pradeep Kiran Sarvepalli

Published Nov 11, 2019• 26 citations
arXivHTMLPDF

Abstract

A quantum secret sharing scheme is a cryptographic protocol by which a dealer can share a secret among a group of $n$ players so that only certain subsets of players can recover the secret by collaboration. In this paper we propose communication efficient quantum threshold secret sharing schemes. They minimize the amount of quantum communication required to reconstruct the secret when more than the necessary number of players collaborate. They are based on a class of staircase codes proposed by Bitar and El Rouayheb. In a standard $((k,n))$ quantum threshold scheme, any subset of $k$ or more players can recover the secret. The quantum communication cost for reconstruction in such schemes is $k$ qudits for each secret qudit. Using the proposed construction, any subset of $d\ensuremath{\ge}k$ players can also collaborate to recover the secret with a communication cost of $d$ qudits for $d\ensuremath{-}k+1$ secret qudits. In other words, for the proposed schemes the quantum communication cost is only $\frac{d}{d\ensuremath{-}k+1}$ qudits for every secret qudit. For $d>k$, proposed schemes are communication efficient with respect to standard schemes; and when $d=2k\ensuremath{-}1$, the quantum communication cost is reduced by a factor $O(k)$. Further, when $n=2k\ensuremath{-}1$, the proposed schemes have optimal communication cost for secret reconstruction.

DOI
10.1103/physreva.100.052313

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A quantum secret sharing scheme is a cryptographic protocol by which a dealer can share a secret among a group of nnn players so that only certain subsets of players can recover the secret by collaboration. In this paper we propose communication efficient quantum threshold secret sharing schemes. They minimize the amount of quantum communication required to reconstruct the secret when more than the necessary number of players collaborate. They are based on a class of staircase codes proposed by Bitar and El Rouayheb. In a standard ((k,n))((k,n))((k,n)) quantum threshold scheme, any subset of kkk or more players can recover the secret. The quantum communication cost for reconstruction in such schemes is kkk qudits for each secret qudit. Using the proposed construction, any subset of d\ensuremath≥kd\ensuremath{\ge}kd\ensuremath≥k players can also collaborate to recover the secret with a communication cost of ddd qudits for d\ensuremath−k+1d\ensuremath{-}k+1d\ensuremath−k+1 secret qudits. In other words, for the proposed schemes the quantum communication cost is only dd\ensuremath−k+1\frac{d}{d\ensuremath{-}k+1}d\ensuremath−k+1d​ qudits for every secret qudit. For d>kd>kd>k, proposed schemes are communication efficient with respect to standard schemes; and when d=2k\ensuremath−1d=2k\ensuremath{-}1d=2k\ensuremath−1, the quantum communication cost is reduced by a factor O(k)O(k)O(k). Further, when n=2k\ensuremath−1n=2k\ensuremath{-}1n=2k\ensuremath−1, the proposed schemes have optimal communication cost for secret reconstruction.
Quantum secret sharing (QSS) is a cryptographic protocol in which a quantum secret is distributed among a number of parties where some subsets of the parties are able to recover the secret while some subsets are unable to recover the secret. In the standard ((k, n)) quantum threshold secret sharing scheme, any subset of k or more parties out of the total n parties can recover the secret while other subsets have no information about the secret. But recovery of the secret incurs a communication cost of at least k qudits for every qudit in the secret. Recently, a class of communication efficient QSS schemes were proposed which can improve this communication cost to dd−k+1\frac{d}{{d - k + 1}}d−k+1d​ by contacting d ≥ k parties where d is fixed prior to the distribution of shares. In this paper, we propose a more general class of ((k, n)) quantum secret sharing schemes with low communication complexity. In these schemes the combiner can contact any d parties at the time of recovery where k ≤ d ≤ n. This is the first such class of universal communication efficient quantum threshold schemes.
A((k,n))((k,n))((k,n))quantum threshold secret sharing (QTS) scheme is a quantum cryptographic protocol for sharing a quantum secret amongnnnparties such that the secret can be recovered by anykkkor more parties whilek−1k-1k−1or fewer parties have no information about the secret. Despite extensive research on these schemes, there has been very little study on optimizing the quantum communication cost during recovery. Recently, we initiated the study of communication efficient quantum threshold secret sharing (CE-QTS) schemes. These schemes reduce the communication complexity in QTS schemes by accessingd>kd>kd>kparties for recovery; heredddis fixed ahead of encoding the secret. In contrast to the standard QTS schemes which requirekkkqudits for recovering each qudit in the secret, these schemes have a lower communication cost ofdd−k+1\frac {d}{d-k+1}d−k+1d​. In this paper, we further develop the theory of communication efficient quantum threshold schemes. Here, we propose universal CE-QTS schemes which reduce the communication cost for alld>kd>kd>ksimultaneously. We provide a framework based on ramp quantum secret sharing to construct CE-QTS and universal CE-QTS schemes. We give another construction for universal CE-QTS schemes based on Staircase codes. We derived a lower bound on communication complexity and show that our constructions are optimal. Finally, an information theoretic model is developed to analyse CE-QTS schemes and the lower bound on communication complexity is proved again using this model.
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.
Secret sharing of a quantum state, or quantum secret sharing, in which a dealer wants to share a 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 shows that our implemented scheme is fully quantum. Moreover, our experimental setup can be treated as a decoding circuit of the five-qubit quantum error-correcting code with two erasure errors.
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 Threshold quantum secret sharing is a cryptography technique for dividing and reconstructing secret information. The dealer shares a secret based on quantum mechanics principles, and a subset of participants cooperate to recover that secret. For example, in k , n quantum threshold scheme and n , n quantum threshold scheme, the former can only reconstruct the secret when at least k shares are collected. The latter requires all n shares to be collected to reconstruct the secret. However, in real scenarios, the priority of participant identities may vary. In order to meet the actual needs of participants with different rights, this paper proposes a w , ω , n quantum secret sharing (QSS) scheme. When the sum of participants’ weights w is greater than or equal to a threshold ω, they can cooperate to reconstruct the secret. In order to achieve this, this paper uses the entangled state of single particles and constructs a verifiable QSS scheme based on the Chinese remainder theorem. Significantly, in case of a dishonest participant, the dealer can delete the participant before recovering the secret to ensure the security of the communication. This scheme is more flexible than other threshold protocols. At the same time, it reduces the communication cost of the participants. In addition, security analysis shows that the scheme resists typical external and internal attacks.