We propose a protocol that enables a dealer to share a quantum secret with n players using less than n quantum shares for several access structures. For threshold schemes we derived an expression that shows how many quantum shares can be saved in this scheme. Also, several features that are available for classical secret-sharing schemes (and previously not known to be possible for quantum secret-sharing) become available with this protocol.
We propose a protocol that enables a dealer to share a quantum secret with n players using less than n quantum shares for several access structures. For threshold schemes we derived an expression that shows how many quantum shares can be saved in this scheme. Also, several features that are available for classical secret-sharing schemes (and previously not known to be possible for quantum secret-sharing) become available with this protocol.
Quantum secret sharing (QSS) allows a dealer to distribute a secret quantum state among a set of parties so that certain subsets can reconstruct the secret, while unauthorized subsets obtain no information. While QSS was introduced over twenty years ago, previous works focused only on existence of perfectly secure schemes, and the share size of the known schemes is exponential even for access structures computed by polynomial size monotone circuits. This stands in contrast to the classical case, where efficient computationally-secure schemes have been long known for all access structures in monotoneP, and one can even obtain shares which are much shorter than the secret which is impossible with perfect security. In this work, we initiate the study of computationally-secure QSS and show that computational assumptions help significantly in building QSS schemes. We present a simple compiler and use it to obtain a large variety results: We construct polynomial-time QSS schemes under standard assumptions for a rich class of access structures. This includes many access structures for which previous results in QSS required exponential share size. We also construct QSS schemes for which the size of the shares is significantly smaller than the size of the secret. As in the classical case, this is impossible with perfect security. We also use our compiler to obtain results beyond computational QSS. In the information-theoretic setting, we improve the share size of perfect QSS schemes for a large class of access structures to 1.5n+o(n), improving upon best known schemes and matching the best known result for general access structures in the classical case. Finally, we show construct efficient schemes for all access structures in P and NP when the quantum secret sharing scheme is given multiple of copies of the secret.
Secret sharing is a cryptographic scheme to encode a secret to multiple shares being distributed to participants, so that only qualified sets of participants can restore the original secret from their shares. When we encode a secret by a secret sharing scheme and distribute shares, sometimes not all participants are accessible, and it is desirable to distribute shares to those participants before a secret information is determined. Secret sharing schemes for classical secrets have been known to be able to distribute some shares before a given secret. Lie et al. found a ((2, 3))-threshold secret sharing for quantum secrets can distribute some shares before a given secret. However, it is unknown whether distributing some shares before a given secret is possible with other access structures of secret sharing for quantum secrets. We propose a quantum secret sharing scheme for quantum secrets that can distribute some shares before a given secret with other access structures.
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.
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.
Quantum secret sharing (QSS) is a cryptographic protocol that leverages quantum mechanics to distribute a secret among multiple parties. With respect to the classical counterpart, in QSS, the secret is encoded into quantum states and shared by a dealer such that only an authorized subsets of participants, i.e., the players, can reconstruct it. Several state-of-the-art studies aim to transpose classical secret sharing into the quantum realm, while maintaining their reliance on traditional network topologies (e.g., star, ring, and fully connected), and require that all thenplayers calculate the secret. These studies exploit the Greenberger–Horne–Zeilinger state, which is a type of maximally entangled quantum state involving three or more qubits. However, none of these works account for redundancy, enhanced security/privacy features, or authentication mechanisms able to fingerprint players. To address these gaps, in this article, we introduce a new concept of QSS, which leans on a generic distributed quantum network, based on a threshold scheme, where all the players collaborate also to the routing of quantum information among them. The dealer, by exploiting a custom flexible weighting system, takes advantage of a newly defined quantum Dijkstra algorithm to select the most suitable subset oftplayers, out of the entire set onnplayers, to involve in the computation. To fingerprint and authenticate users, CRYSTAL-Kyber primitives are adopted, while also protecting each player’s privacy by hiding their identities. We show the effectiveness and performance of the proposed protocol by testing it against the main classical and quantum attacks, thereby improving the state-of-the-art security measures.
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.