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arXiv:1506.02966 · Physical Review A

Quantum secret sharing and random hopping: Using single states instead of entanglement

Vahid Karimipour, M. Asoudeh

Published Sep 2, 2015• 67 citations
arXivHTMLPDF

Abstract

Quantum secret sharing (QSS) protocols between $N$ players, for sharing classical secrets, either use multipartite entangled states or use sequential manipulation of single $d$-level states only when $d$ is prime (A. Tavakoli et al., arXiv:1501.05582). We propose a sequential scheme which is valid for any value of $d$. In contrast to A. Tavakoli et al. whose efficiency (number of valid rounds) is $\frac{1}{d}$, the efficiency of our scheme is $\frac{1}{2}$ for any $d$. This, together with the fact that in the limit $d\ensuremath{\longrightarrow}\ensuremath{\infty}$ the scheme can be implemented by continuous variable optical states, brings the scheme into the domain of present day technology.

DOI
10.1103/physreva.92.030301

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Quantum secret sharing (QSS) protocols between NNN players, for sharing classical secrets, either use multipartite entangled states or use sequential manipulation of single ddd-level states only when ddd is prime (A. Tavakoli et al., arXiv:1501.05582). We propose a sequential scheme which is valid for any value of ddd. In contrast to A. Tavakoli et al. whose efficiency (number of valid rounds) is 1d\frac{1}{d}d1​, the efficiency of our scheme is 12\frac{1}{2}21​ for any ddd. This, together with the fact that in the limit d\ensuremath⟶\ensuremath∞d\ensuremath{\longrightarrow}\ensuremath{\infty}d\ensuremath⟶\ensuremath∞ the scheme can be implemented by continuous variable optical states, brings the scheme into the domain of present day technology.
Quantum secret sharing (QSS), as a quantum extension of classical secret sharing, uses the basic principles of quantum mechanics to share information safely among multiple parties, providing a new paradigm for information security. As a key foundation for secure multiparty quantum communication and distributed quantum computing, QSS has attracted considerable attention since its emergence. Currently, research in this field includes both classical and quantum scenarios, and continuous progress has been made in both theoretical and experimental aspects. This paper first reviews the current development of QSS for classical information. In this regard, significant and parallel progress has been made in both discrete-variable QSS and continuous-variable QSS. The QSS protocols for sharing classical information, from entangled states to single photons and then to coherent light, have been continuously optimized to better utilize available resources and achieve more efficient implementation under current technological conditions. Meanwhile, round-robin, measurement-device-independent, and other protocols have been steadily improving the security of QSS. Next, one will focus on QSS scheme for quantum secrets, which begins with the symmetry of access structures and introduces basic (k, n) threshold protocols, dynamic schemes that support adaptive agent groups, and symmetric quantum information splitting through entanglement. It further introduces hierarchical quantum secret sharing schemes for asymmetric splitting of quantum information. Considering practical laboratory conditions of quantum states as resources, an overall discussion is conducted on quantum secret sharing with graph states. Afterwards, the design of a continuous-variable scheme for quantum secret sharing is outlined, and entanglement state sharing and quantum teleportation between multiple senders and receivers are introduced. Finally, this review discusses and outlines the future development directions of QSS, thereby inspiring readers to further study and explore the relevant subjects.
Sequential Quantum Secret Sharing schemes (QSS) do not use entangled states for secret sharing, rather they rely on sequential operations of the players on a single state which is circulated between the players. In order to check the viability of these schemes under imperfect operations and noise in the channels, we consider one such scheme in detail and show that under moderate conditions it is still possible to extract viable secure shared keys in this scheme. Although we specifically consider only one type of sequential scheme and three different noise models, our method is fairly general to be applied to other QSS schemes and noise models as well.
A quantum secret sharing (QSS) scheme with single photons was proposed, the trusted third party (TTP) encoded the secret value into conjugate single quantum states, in the revealing phase each participant performs the corresponding unitary operation on the single photon sequence sequentially according to its’ private key, and the participants can recover the secret value only through one round of interaction with the TTP and two round of interactions between themselves, further more any dishonest action and malicious attack can be detected.
We give an example of a wide class of problems for which quantum-information protocols based on multisystem entanglement can be mapped into much simpler ones involving one system. Secret sharing is a cryptographic primitive which plays a central role in various secure multiparty computation tasks and management of keys in cryptography. In secret sharing protocols, a classical message is divided into shares given to recipient parties in such a way that some number of parties need to collaborate in order to reconstruct the message. Quantum protocols for the task commonly rely on multipartite GHZ entanglement. We present a multiparty secret sharing protocol which requires only sequential communication of a single quantum ddd-level system (for any prime ddd). It has huge advantages in scalability and can be realized with state-of-the-art technology.
Abstract In this paper we propose a novel and efficient quantum secret sharing protocol using d-level single particle, which it can realize a general access structure via the thought of concatenation. In addition, Our scheme includes all advantages of Tavakoli’s scheme [Phys. Rev. A 92 (2015) 030302(R)]. In contrast to Tavakoli’s scheme, the efficiency of our scheme is 1 for the same situation, and the access structure is more general and has advantages in practical significance. Furthermore, we also analyze the security of our scheme in the primary quantum attacks.
The need for secrecy and security is essential in communication. Secret sharing is a conventional protocol to distribute a secret message to a group of parties, who cannot access it individually but need to cooperate in order to decode it. While several variants of this protocol have been investigated, including realizations using quantum systems, the security of quantum secret sharing schemes against eavesdroppers and dishonest participants remained unproven. Here we establish an unconditional security proof for continuous variable entanglement-based quantum secret sharing schemes, in the limit of asymptotic keys and for an arbitrary number of players, by utilizing ideas from the recently developed one-sided device-independent approach to quantum key distribution. We demonstrate the practical feasibility of our scheme, which can be implemented by Gaussian states and homodyne measurements, with no need for ideal single-photon sources or quantum memories. Our results establish quantum secret sharing as a viable and practically relevant primitive for quantum communication technologies.