2,268 research outputs found
On the optimization of bipartite secret sharing schemes
Optimizing the ratio between the maximum length of the shares and the length of the secret value in secret sharing schemes for general access structures is an extremely difficult and long-standing open problem. In this paper, we study it for bipartite access structures, in which the set of participants is divided in two parts, and all participants in each part play an equivalent role. We focus on the search of lower bounds by using a special class of polymatroids that is introduced here, the tripartite ones. We present a method based on linear programming to compute, for every given bipartite access structure, the best lower bound that can be obtained by this combinatorial method. In addition, we obtain some general lower bounds that improve the previously known ones, and we construct optimal secret sharing schemes for a family of bipartite access structures.Peer ReviewedPostprint (author's final draft
An Epitome of Multi Secret Sharing Schemes for General Access Structure
Secret sharing schemes are widely used now a days in various applications,
which need more security, trust and reliability. In secret sharing scheme, the
secret is divided among the participants and only authorized set of
participants can recover the secret by combining their shares. The authorized
set of participants are called access structure of the scheme. In Multi-Secret
Sharing Scheme (MSSS), k different secrets are distributed among the
participants, each one according to an access structure. Multi-secret sharing
schemes have been studied extensively by the cryptographic community. Number of
schemes are proposed for the threshold multi-secret sharing and multi-secret
sharing according to generalized access structure with various features. In
this survey we explore the important constructions of multi-secret sharing for
the generalized access structure with their merits and demerits. The features
like whether shares can be reused, participants can be enrolled or dis-enrolled
efficiently, whether shares have to modified in the renewal phase etc., are
considered for the evaluation
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
On Ideal Secret-Sharing Schemes for -homogeneous access structures
A -uniform hypergraph is a hypergraph where each -hyperedge has exactly
vertices. A -homogeneous access structure is represented by a
-uniform hypergraph , in which the participants correspond to
the vertices of hypergraph . A set of vertices can reconstruct the
secret value from their shares if they are connected by a -hyperedge, while
a set of non-adjacent vertices does not obtain any information about the
secret. One parameter for measuring the efficiency of a secret sharing scheme
is the information rate, defined as the ratio between the length of the secret
and the maximum length of the shares given to the participants. Secret sharing
schemes with an information rate equal to one are called ideal secret sharing
schemes. An access structure is considered ideal if an ideal secret sharing
scheme can realize it. Characterizing ideal access structures is one of the
important problems in secret sharing schemes. The characterization of ideal
access structures has been studied by many authors~\cite{BD, CT,JZB,
FP1,FP2,DS1,TD}. In this paper, we characterize ideal -homogeneous access
structures using the independent sequence method. In particular, we prove that
the reduced access structure of is an -threshold access
structure when the optimal information rate of is larger than
, where is a -homogeneous access structure
satisfying specific criteria.Comment: 19 page
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