57,348 research outputs found
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
Non-Threshold Quantum Secret Sharing Schemes in the Graph State Formalism
In a recent work, Markham and Sanders have proposed a framework to study
quantum secret sharing (QSS) schemes using graph states. This framework unified
three classes of QSS protocols, namely, sharing classical secrets over private
and public channels, and sharing quantum secrets. However, most work on secret
sharing based on graph states focused on threshold schemes. In this paper, we
focus on general access structures. We show how to realize a large class of
arbitrary access structures using the graph state formalism. We show an
equivalence between binary quantum codes and graph state secret
sharing schemes sharing one bit. We also establish a similar (but restricted)
equivalence between a class of Calderbank-Shor-Steane (CSS) codes and
graph state QSS schemes sharing one qubit. With these results we are able to
construct a large class of quantum secret sharing schemes with arbitrary access
structures.Comment: LaTeX, 6 page
Secret Sharing Schemes with General Access Structures (Full version)
Secret sharing schemes with general monotone access structures have been widely discussed in the literature. But in some scenarios, non-monotone access structures may have more practical significance. In this paper, we shed a new light on secret sharing schemes realizing general (not necessarily monotone) access structures. Based on an attack model for secret sharing schemes with general access structures, we redefine perfect secret sharing schemes, which is a generalization of the known concept of perfect secret sharing schemes with monotone access structures. Then, we provide for the first time two constructions of perfect secret sharing schemes with general access structures. The first construction can be seen as a democratic scheme in the sense that the shares are generated by the players themselves.
Our second construction significantly enhance the efficiency of the system, where the shares are distributed by the trusted center (TC)
Computational Quantum Secret Sharing
Quantum secret sharing (QSS) allows a dealer to distribute a secret quantum state among a set of parties in such a way that certain authorized subsets can reconstruct the secret, while unauthorized subsets obtain no information about it. Previous works on QSS for general access structures focused solely on the existence of perfectly secure schemes, and the share size of the known schemes is necessarily exponential even in cases where the access structure is computed by polynomial size monotone circuits. This stands in stark contrast to the classical setting, where polynomial-time computationally-secure secret sharing schemes have been long known for all access structures computed by polynomial-size monotone circuits under standard hardness assumptions, and one can even obtain shares which are much shorter than the secret (which is impossible with perfect security).
While QSS was introduced over twenty years ago, previous works only considered information-theoretic privacy. In this work, we initiate the study of computationally-secure QSS and show that computational assumptions help significantly in building QSS schemes, just as in the classical case. We present a simple compiler and use it to obtain a large variety results: We construct polynomial-time computationally-secure QSS schemes under standard hardness assumptions for a rich class of access structures. This includes many access structures for which previous results in QSS necessarily required exponential share size. In fact, we can go even further: We construct QSS schemes for which the size of the quantum shares is significantly smaller than the size of the secret. As in the classical setting, this is impossible with perfect security.
We also apply 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 n-party access structures to 1.5^{n+o(n)}, improving upon best known schemes and matching the best known result for general access structures in the classical setting. Finally, among other things, we study the class of access structures which can be efficiently implemented when the quantum secret sharing scheme has access to a given number of copies of the secret, including all such functions in ? and NP
Function and secret sharing extensions for Blakley and Asmuth-Bloom secret sharing schemes
Ankara : The Department of Computer Engineering and the Institute of Engineering and Science of Bilkent University, 2009.Thesis (Master's) -- Bilkent University, 2009.Includes bibliographical references leaves 65-69.Threshold cryptography deals with situations where the authority to initiate or
perform cryptographic operations is distributed amongst a group of individuals.
Usually in these situations a secret sharing scheme is used to distribute shares
of a highly sensitive secret, such as the private key of a bank, to the involved
individuals so that only when a sufficient number of them can reconstruct the
secret but smaller coalitions cannot. The secret sharing problem was introduced
independently by Blakley and Shamir in 1979. They proposed two different solutions.
Both secret sharing schemes (SSS) are examples of linear secret sharing.
Many extensions and solutions based on these secret sharing schemes have appeared
in the literature, most of them using Shamir SSS. In this thesis, we apply
these ideas to Blakley secret sharing scheme.
Many of the standard operations of single-user cryptography have counterparts
in threshold cryptography. Function sharing deals with the problem of
distribution of the computation of a function (such as decryption or signature)
among several parties. The necessary values for the computation are distributed
to the participants using a secret sharing scheme. Several function sharing
schemes have been proposed in the literature with most of them using Shamir
secret sharing as the underlying SSS. In this work, we investigate how function
sharing can be achieved using linear secret sharing schemes in general and give
solutions of threshold RSA signature, threshold Paillier decryption and threshold
DSS signature operations. The threshold RSA scheme we propose is a generalization
of Shoup’s Shamir-based scheme. It is similarly robust and provably secure
under the static adversary model.
In threshold cryptography the authorization of groups of people are decided simply according to their size. There are also general access structures in which
any group can be designed as authorized. Multipartite access structures constitute
an example of general access structures in which members of a subset are
equivalent to each other and can be interchanged. Multipartite access structures
can be used to represent any access structure since all access structures are multipartite.
To investigate secret sharing schemes using these access structures,
we used Mignotte and Asmuth-Bloom secret sharing schemes which are based
on the Chinese remainder theorem (CRT). The question we tried to asnwer was
whether one can find a Mignotte or Asmuth-Bloom sequence for an arbitrary
access structure. For this purpose, we adapted an algorithm that appeared in the
literature to generate these sequences. We also proposed a new SSS which solves
the mentioned problem by generating more than one sequence.Bozkurt, İlker NadiM.S
Stronger Leakage-Resilient and Non-Malleable Secret-Sharing Schemes for General Access Structures
In this work we present a collection of compilers that take secret sharing schemes for an arbitrary access structures as input and produce either leakage-resilient or non-malleable secret sharing schemes for the same access structure. A leakage-resilient secret sharing scheme hides the secret from an adversary, who has access to an unqualified set of shares, even if the adversary additionally obtains some size-bounded leakage from all other secret shares. A non-malleable secret sharing scheme guarantees that a secret that is reconstructed from a set of tampered shares is either equal to the original secret or completely unrelated. To the best of our knowledge we present the first generic compiler for leakage-resilient secret sharing for general access structures. In the case of non-malleable secret sharing, we strengthen previous definitions, provide separations between them, and construct a non-malleable secret sharing scheme for general access structures that fulfills the strongest definition with respect to independent share tampering functions. More precisely, our scheme is secure against concurrent tampering: The adversary is allowed to (non-adaptively) tamper the shares multiple times, and in each tampering attempt can freely choose the qualified set of shares to be used by the reconstruction algorithm to re-construct the tampered secret. This is a strong analogue of the multiple-tampering setting for split-state non-malleable codes and extractors.
We show how to use leakage-resilient and non-malleable secret sharing schemes to construct leakage-resilient and non-malleable threshold signatures. Classical threshold signatures allow to distribute the secret key of a signature scheme among a set of parties, such that certain qualified subsets can sign messages. We construct threshold signature schemes that remain secure even if an adversary leaks from or tampers with all secret shares
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