423 research outputs found
Secret Sharing Schemes with a large number of players from Toric Varieties
A general theory for constructing linear secret sharing schemes over a finite
field \Fq from toric varieties is introduced. The number of players can be as
large as for . We present general methods for obtaining
the reconstruction and privacy thresholds as well as conditions for
multiplication on the associated secret sharing schemes.
In particular we apply the method on certain toric surfaces. The main results
are ideal linear secret sharing schemes where the number of players can be as
large as . We determine bounds for the reconstruction and privacy
thresholds and conditions for strong multiplication using the cohomology and
the intersection theory on toric surfaces.Comment: 15 pages, 4 figures. arXiv admin note: text overlap with
arXiv:1203.454
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
Quantum-classical complexity-security tradeoff in secure multiparty computations
I construct a secure multiparty scheme to compute a classical function by a succinct use of a specially designed fault-tolerant random polynomial quantum error correction code. This scheme is secure provided that (asymptotically) strictly more than five-sixths of the players are honest. Moreover, the security of this scheme follows directly from the theory of quantum error correcting code, and hence is valid without any computational assumption. I also discuss the quantum-classical complexity-security tradeoff in secure multiparty computation schemes and argue why a full-blown quantum code is necessary in my scheme.published_or_final_versio
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