2,807 research outputs found
Linear Secret-Sharing Schemes for Forbidden Graph Access Structures
A secret-sharing scheme realizes the forbidden graph access structure determined by a graph if the parties are the vertices of the graph and the subsets that can reconstruct the secret are the pairs of vertices in (i.e., the edges) and the subsets of at least three vertices. Secret-sharing schemes for forbidden graph access structures defined by bipartite graphs are equivalent to conditional disclosure of secrets protocols.
We study the complexity of realizing a forbidden graph access structure by linear secret-sharing schemes. A secret-sharing scheme is linear if the secret can be reconstructed from the shares by a linear mapping. We provide efficient constructions and lower bounds on the share size of linear secret-sharing schemes for sparse and dense graphs, closing the gap between upper and lower bounds. Given a sparse (resp. dense) graph with vertices and at most edges (resp. at least edges), for some , we construct a linear secret-sharing scheme realizing its forbidden graph access structure in which the total size of the shares is . Furthermore, we construct linear secret-sharing schemes realizing these access structures in which the size of each share is . We also provide constructions achieving different trade-offs between the size of each share and the total share size.
We prove that almost all forbidden graph access structures require linear secret-sharing schemes with total share size ; this shows that the construction of Gay, Kerenidis, and Wee [CRYPTO 2015] is optimal. Furthermore, we show that for every there exist a graph with at most edges and a graph with at least edges such that the total share size in any linear secret-sharing scheme realizing the associated forbidden graph access structures is . Finally, we show that for every there exist a graph with at most edges and a graph with at least edges such that the size of the share of at least one party in any linear secret-sharing scheme realizing these forbidden graph access structures is . This shows that our constructions are optimal (up to poly-logarithmic factors)
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
Probabilistic Infinite Secret Sharing
The study of probabilistic secret sharing schemes using arbitrary probability
spaces and possibly infinite number of participants lets us investigate
abstract properties of such schemes. It highlights important properties,
explains why certain definitions work better than others, connects this topic
to other branches of mathematics, and might yield new design paradigms.
A probabilistic secret sharing scheme is a joint probability distribution of
the shares and the secret together with a collection of secret recovery
functions for qualified subsets. The scheme is measurable if the recovery
functions are measurable. Depending on how much information an unqualified
subset might have, we define four scheme types: perfect, almost perfect, ramp,
and almost ramp. Our main results characterize the access structures which can
be realized by schemes of these types.
We show that every access structure can be realized by a non-measurable
perfect probabilistic scheme. The construction is based on a paradoxical pair
of independent random variables which determine each other.
For measurable schemes we have the following complete characterization. An
access structure can be realized by a (measurable) perfect, or almost perfect
scheme if and only if the access structure, as a subset of the Sierpi\'nski
space , is open, if and only if it can be realized by a span
program. The access structure can be realized by a (measurable) ramp or almost
ramp scheme if and only if the access structure is a set
(intersection of countably many open sets) in the Sierpi\'nski topology, if and
only if it can be realized by a Hilbert-space program
Matroids and Quantum Secret Sharing Schemes
A secret sharing scheme is a cryptographic protocol to distribute a secret
state in an encoded form among a group of players such that only authorized
subsets of the players can reconstruct the secret. Classically, efficient
secret sharing schemes have been shown to be induced by matroids. Furthermore,
access structures of such schemes can be characterized by an excluded minor
relation. No such relations are known for quantum secret sharing schemes. In
this paper we take the first steps toward a matroidal characterization of
quantum secret sharing schemes. In addition to providing a new perspective on
quantum secret sharing schemes, this characterization has important benefits.
While previous work has shown how to construct quantum secret sharing schemes
for general access structures, these schemes are not claimed to be efficient.
In this context the present results prove to be useful; they enable us to
construct efficient quantum secret sharing schemes for many general access
structures. More precisely, we show that an identically self-dual matroid that
is representable over a finite field induces a pure state quantum secret
sharing scheme with information rate one
Secret sharing schemes for ports of matroids of rank 3
summary:A secret sharing scheme is ideal if the size of each share is equal to the size of the secret. Brickell and Davenport showed that the access structure of an ideal secret sharing scheme is determined by a matroid. Namely, the minimal authorized subsets of an ideal secret sharing scheme are in correspondence with the circuits of a matroid containing a fixed point. In this case, we say that the access structure is a matroid port. It is known that, for an access structure, being a matroid port is not a sufficient condition to admit an ideal secret sharing scheme. In this work we present a linear secret sharing scheme construction for ports of matroids of rank 3 in which the size of each share is at most times the size of the secret. Using the previously known secret sharing constructions, the size of each share was the size of the secret. Our construction is extended to ports of matroids of any rank , obtaining secret sharing schemes in which the size of each share is at most times the size of the secret. This work is complemented by presenting lower bounds: There exist matroid ports that require -linear secret schemes with total information ratio
Practical sharing of quantum secrets over untrusted channels
In this work we address the issue of sharing a quantum secret over untrusted
channels between the dealer and players. Existing methods require entanglement
over a number of systems which scales with the security parameter, quickly
becoming impractical. We present protocols (interactive and a non-interactive)
where single copy encodings are sufficient. Our protocols work for all quantum
secret sharing schemes and access structures, and are implementable with
current experimental set ups. For a single authorised player, our protocols act
as quantum authentication protocols
Ideal homogeneous access structures constructed from graphs
Starting from a new relation between graphs and secret sharing schemes introduced by Xiao, Liu and Zhang, we show a method to construct more general ideal homogeneous access structures. The method has some advantages: it efficiently gives an ideal homogeneous access structure for the desired rank, and some conditions can be imposed (such as forbidden or necessary subsets of players), even if the exact composition of the resulting access structure cannot be fully controlled. The number of homogeneous access structures that can be constructed in this way is quite limited; for example, we show that (t, l)-threshold access structures can be constructed from a graph only when t = 1, t = l - 1 or t = l.Peer ReviewedPostprint (published version
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
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