9,379 research outputs found
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
Relative generalized Hamming weights of one-point algebraic geometric codes
Security of linear ramp secret sharing schemes can be characterized by the
relative generalized Hamming weights of the involved codes. In this paper we
elaborate on the implication of these parameters and we devise a method to
estimate their value for general one-point algebraic geometric codes. As it is
demonstrated, for Hermitian codes our bound is often tight. Furthermore, for
these codes the relative generalized Hamming weights are often much larger than
the corresponding generalized Hamming weights
Infinite Secret Sharing -- Examples
The motivation for extending secret sharing schemes to cases when either the
set of players is infinite or the domain from which the secret and/or the
shares are drawn is infinite or both, is similar to the case when switching to
abstract probability spaces from classical combinatorial probability. It might
shed new light on old problems, could connect seemingly unrelated problems, and
unify diverse phenomena.
Definitions equivalent in the finitary case could be very much different when
switching to infinity, signifying their difference. The standard requirement
that qualified subsets should be able to determine the secret has different
interpretations in spite of the fact that, by assumption, all participants have
infinite computing power. The requirement that unqualified subsets should have
no, or limited information on the secret suggests that we also need some
probability distribution. In the infinite case events with zero probability are
not necessarily impossible, and we should decide whether bad events with zero
probability are allowed or not.
In this paper, rather than giving precise definitions, we enlist an abundance
of hopefully interesting infinite secret sharing schemes. These schemes touch
quite diverse areas of mathematics such as projective geometry, stochastic
processes and Hilbert spaces. Nevertheless our main tools are from probability
theory. The examples discussed here serve as foundation and illustration to the
more theory oriented companion paper
An Economic Analysis of Privacy Protection and Statistical Accuracy as Social Choices
Statistical agencies face a dual mandate to publish accurate statistics while protecting respondent privacy. Increasing privacy protection requires decreased accuracy. Recognizing this as a resource allocation problem, we propose an economic solution: operate where the marginal cost of increasing privacy equals the marginal benefit. Our model of production, from computer science, assumes data are published using an efficient differentially private algorithm. Optimal choice weighs the demand for accurate statistics against the demand for privacy. Examples from U.S. statistical programs show how our framework can guide decision-making. Further progress requires a better understanding of willingness-to-pay for privacy and statistical accuracy
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