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arXiv:1501.05582 · Physical Review A

Secret sharing with a single d -level quantum system

Armin Tavakoli, Isabelle Herbauts, Marek Żukowski, Mohamed Bourennane

Published Sep 21, 2015• 142 citations
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Abstract

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 $d$-level system (for any prime $d$). It has huge advantages in scalability and can be realized with state-of-the-art technology.

DOI
10.1103/physreva.92.030302

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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.
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Quantum secret sharing is a basic quantum cryptographic primitive, which plays an important role in robust key management and secure multiparty computation etc. In this work, we give a cryptanalysis of efficient controlled semi-quantum secret sharing protocol with entangled states proposed recently, which shows that the controller can recover the secret if he cooperates with any one participant. Furthermore, an external opponent can make participants recover a false secret without being detected by a special denial-of-service attack. Therefore, this protocol does not satisfy the security requirement that any unauthorized set can gain access to no information on the secret and cannot guarantee its correctness.
Abstract Quantum secret sharing is a basic quantum cryptographic primitive, which has a lot of applications in information security and privacy preservation. An efficient multiparty quantum secret sharing protocol [EPJ Quantum Technology 2023 10: 29] based on a novel structure and single qubits was reported recently. In this paper, we give a cryptanalysis of this protocol and show that it cannot satisfy the security requirement for secret sharing because an unauthorized set of agents can gain access to some information on the dealer's secret by a special collusion attack. Furthermore, we put forward an effective way to deal with the security problem.
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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.
Efficient Multiparty Quantum Key Agreement With a Single ddd -Level Quantum System Secure Against Collusive Attack
Recently, multiparty quantum key agreement (MQKA) protocols have gained increasing attention. Several MQKA protocols in the traveling mode have been proposed for higher key generation rates, which, however, are vulnerable to a collusive attack presented by Liu. In this paper, an analysis of Liu's collusive attacks on Cao et al.'s protocol is given, based on which an efficient MQKA protocol that requires only sequential communication of a single d-level quantum system is put forward. Because of the single d-level quantum system, our protocol has huge advantages in scalability and can be realized with the state-of-the-art technology. The scalability means that each additional participant is only required to perform a unitary operator that is comparatively simple, and the complexity of measurements remains independent of the number of participants. Our protocol can also resist Liu's collusive attacks due to the encrypted quantum channel and has an efficiency rate of 1/2N(N is the number of participants) that is much better than those of other quantum key agreement protocols. In addition, by using the proposed encoding method, a wide class of problems for which quantum information protocols based on multisystem entanglement can be mapped into much simpler ones involving only one system.