93 research outputs found
Message Randomization and Strong Security in Quantum Stabilizer-Based Secret Sharing for Classical Secrets
We improve the flexibility in designing access structures of quantum
stabilizer-based secret sharing schemes for classical secrets, by introducing
message randomization in their encoding procedures. We generalize the
Gilbert-Varshamov bound for deterministic encoding to randomized encoding of
classical secrets. We also provide an explicit example of a ramp secret sharing
scheme with which multiple symbols in its classical secret are revealed to an
intermediate set, and justify the necessity of incorporating strong security
criterion of conventional secret sharing. Finally, we propose an explicit
construction of strongly secure ramp secret sharing scheme by quantum
stabilizers, which can support twice as large classical secrets as the
McEliece-Sarwate strongly secure ramp secret sharing scheme of the same share
size and the access structure.Comment: Publisher's Open Access PDF. arXiv admin note: text overlap with
arXiv:1811.0521
Quantum Stabilizer Codes Can Realize Access Structures Impossible by Classical Secret Sharing
We show a simple example of a secret sharing scheme encoding classical secret
to quantum shares that can realize an access structure impossible by classical
information processing with limitation on the size of each share. The example
is based on quantum stabilizer codes.Comment: LaTeX2e, 5 pages, no figure. Comments from readers are welcom
Advance sharing of quantum shares for classical secrets
Secret sharing schemes for classical secrets can be classified into classical
secret sharing schemes and quantum secret sharing schemes. Classical secret
sharing has been known to be able to distribute some shares before a given
secret. On the other hand, quantum mechanics extends the capabilities of secret
sharing beyond those of classical secret sharing. We propose quantum secret
sharing with the capabilities in designing of access structures more flexibly
and realizing higher efficiency beyond those of classical secret sharing, that
can distribute some shares before a given secret.Comment: 11 pages, 1 figure, 1 table. Publisher's open access PDF. Results
unchanged. This research was in part presented at QCrypt 2022, Taipei City,
Taiwan, August 29-September 2, 202
Approximate Quantum Error-Correcting Codes and Secret Sharing Schemes
It is a standard result in the theory of quantum error-correcting codes that
no code of length n can fix more than n/4 arbitrary errors, regardless of the
dimension of the coding and encoded Hilbert spaces. However, this bound only
applies to codes which recover the message exactly. Naively, one might expect
that correcting errors to very high fidelity would only allow small violations
of this bound. This intuition is incorrect: in this paper we describe quantum
error-correcting codes capable of correcting up to (n-1)/2 arbitrary errors
with fidelity exponentially close to 1, at the price of increasing the size of
the registers (i.e., the coding alphabet). This demonstrates a sharp
distinction between exact and approximate quantum error correction. The codes
have the property that any components reveal no information about the
message, and so they can also be viewed as error-tolerant secret sharing
schemes.
The construction has several interesting implications for cryptography and
quantum information theory. First, it suggests that secret sharing is a better
classical analogue to quantum error correction than is classical error
correction. Second, it highlights an error in a purported proof that verifiable
quantum secret sharing (VQSS) is impossible when the number of cheaters t is
n/4. More generally, the construction illustrates a difference between exact
and approximate requirements in quantum cryptography and (yet again) the
delicacy of security proofs and impossibility results in the quantum model.Comment: 14 pages, no figure
Experimental demonstration of graph-state quantum secret sharing
Distributed quantum communication and quantum computing offer many new
opportunities for quantum information processing. Here networks based on highly
nonlocal quantum resources with complex entanglement structures have been
proposed for distributing, sharing and processing quantum information. Graph
states in particular have emerged as powerful resources for such tasks using
measurement-based techniques. We report an experimental demonstration of
graph-state quantum secret sharing, an important primitive for a quantum
network. We use an all-optical setup to encode quantum information into photons
representing a five-qubit graph state. We are able to reliably encode,
distribute and share quantum information between four parties. In our
experiment we demonstrate the integration of three distinct secret sharing
protocols, which allow for security and protocol parameters not possible with
any single protocol alone. Our results show that graph states are a promising
approach for sophisticated multi-layered protocols in quantum networks
- …