44,356 research outputs found
A Study on Multisecret-Sharing Schemes Based on Linear Codes
Secret sharing has been a subject of study since 1979. In the secret sharing schemes there are some participants and a dealer. The dealer chooses a secret. The main principle is to distribute a secret amongst a group of participants. Each of whom is called a share of the secret. The secret can be retrieved by participants. Clearly the participants combine their shares to reach the secret. One of the secret sharing schemes is threshold secret sharing scheme. A threshold secret sharing scheme is a method of distribution of information among participants such that can recover the secret but cannot. The coding theory has been an important role in the constructing of the secret sharing schemes. Since the code of a symmetric design is a linear code, this study is about the multisecret-sharing schemes based on the dual code of code of a symmetric design. We construct a multisecret-sharing scheme Blakley’s construction of secret sharing schemes using the binary codes of the symmetric design. Our scheme is a threshold secret sharing scheme. The access structure of the scheme has been described and shows its connection to the dual code. Furthermore, the number of minimal access elements has been formulated under certain conditions. We explain the security of this scheme
On the information ratio of non-perfect secret sharing schemes
The final publication is available at Springer via http://dx.doi.org/10.1007/s00453-016-0217-9A secret sharing scheme is non-perfect if some subsets of players that cannot recover the secret value have partial information about it. The information ratio of a secret sharing scheme is the ratio between the maximum length of the shares and the length of the secret. This work is dedicated to the search of bounds on the information ratio of non-perfect secret sharing schemes and the construction of efficient linear non-perfect secret sharing schemes. To this end, we extend the known connections between matroids, polymatroids and perfect secret sharing schemes to the non-perfect case. In order to study non-perfect secret sharing schemes in all generality, we describe their structure through their access function, a real function that measures the amount of information on the secret value that is obtained by each subset of players. We prove that there exists a secret sharing scheme for every access function. Uniform access functions, that is, access functions whose values depend only on the number of players, generalize the threshold access structures. The optimal information ratio of the uniform access functions with rational values has been determined by Yoshida, Fujiwara and Fossorier. By using the tools that are described in our work, we provide a much simpler proof of that result and we extend it to access functions with real values.Peer ReviewedPostprint (author's final draft
Optimal Information Rate of Secret Sharing Schemes on Trees
The information rate for an access structure is the reciprocal of the load of the optimal secret sharing scheme for this structure. We determine this value for all trees: it is (2 - 1/c)(-1), where is the size of the largest core of the tree. A subset of the vertices of a tree is a core if it induces a connected subgraph and for each vertex in the subset one finds a neighbor outside the subset. Our result follows from a lower and an upper bound on the information rate that applies for any graph and happen to coincide for trees because of a correspondence between the size of the largest core and a quantity related to a fractional cover of the tree with stars
On the Download Rate of Homomorphic Secret Sharing
A homomorphic secret sharing (HSS) scheme is a secret sharing scheme that
supports evaluating functions on shared secrets by means of a local mapping
from input shares to output shares. We initiate the study of the download rate
of HSS, namely, the achievable ratio between the length of the output shares
and the output length when amortized over function evaluations. We
obtain the following results.
* In the case of linear information-theoretic HSS schemes for degree-
multivariate polynomials, we characterize the optimal download rate in terms of
the optimal minimal distance of a linear code with related parameters. We
further show that for sufficiently large (polynomial in all problem
parameters), the optimal rate can be realized using Shamir's scheme, even with
secrets over .
* We present a general rate-amplification technique for HSS that improves the
download rate at the cost of requiring more shares. As a corollary, we get
high-rate variants of computationally secure HSS schemes and efficient private
information retrieval protocols from the literature.
* We show that, in some cases, one can beat the best download rate of linear
HSS by allowing nonlinear output reconstruction and error
probability
Quantum Strongly Secure Ramp Secret Sharing
Quantum secret sharing is a scheme for encoding a quantum state (the secret)
into multiple shares and distributing them among several participants. If a
sufficient number of shares are put together, then the secret can be fully
reconstructed. If an insufficient number of shares are put together however, no
information about the secret can be revealed. In quantum ramp secret sharing,
partial information about the secret is allowed to leak to a set of
participants, called an unqualified set, that cannot fully reconstruct the
secret. By allowing this, the size of a share can be drastically reduced. This
paper introduces a quantum analog of classical strong security in ramp secret
sharing schemes. While the ramp secret sharing scheme still leaks partial
information about the secret to unqualified sets of participants, the strong
security condition ensures that qudits with critical information can no longer
be leaked.Comment: svjour3.cls, 14 pages, 1 figure. Versions 1&2 were wrong. V3 is
mathematically correct. The first author was moved to the secon
Secret sharing schemes: Optimizing the information ratio
Secret sharing refers to methods used to distribute a secret value among a set of participants. This work deals with the optimization of two parameters regarding the efficiency of a secret sharing scheme: the information ratio and average information ratio. Only access structures (a special family of sets) on 5 and 6 participants will be considered. First, access structures with 5 participants will be studied, followed by the ones on 6 participants that are based on graphs. The main goal of the paper is to check existing lower bounds (and improve some of them) by using linear programs with the sage solver. Shannon information inequalities have been used to translate the polymatroid axioms into linear constraints
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