16,003 research outputs found
Almost-perfect secret sharing
Splitting a secret s between several participants, we generate (for each
value of s) shares for all participants. The goal: authorized groups of
participants should be able to reconstruct the secret but forbidden ones get no
information about it. In this paper we introduce several notions of non-
perfect secret sharing, where some small information leak is permitted. We
study its relation to the Kolmogorov complexity version of secret sharing
(establishing some connection in both directions) and the effects of changing
the secret size (showing that we can decrease the size of the secret and the
information leak at the same time).Comment: Acknowledgments adde
Security in Locally Repairable Storage
In this paper we extend the notion of {\em locally repairable} codes to {\em
secret sharing} schemes. The main problem that we consider is to find optimal
ways to distribute shares of a secret among a set of storage-nodes
(participants) such that the content of each node (share) can be recovered by
using contents of only few other nodes, and at the same time the secret can be
reconstructed by only some allowable subsets of nodes. As a special case, an
eavesdropper observing some set of specific nodes (such as less than certain
number of nodes) does not get any information. In other words, we propose to
study a locally repairable distributed storage system that is secure against a
{\em passive eavesdropper} that can observe some subsets of nodes.
We provide a number of results related to such systems including upper-bounds
and achievability results on the number of bits that can be securely stored
with these constraints.Comment: This paper has been accepted for publication in IEEE Transactions of
Information Theor
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
Secret-Sharing for NP
A computational secret-sharing scheme is a method that enables a dealer, that
has a secret, to distribute this secret among a set of parties such that a
"qualified" subset of parties can efficiently reconstruct the secret while any
"unqualified" subset of parties cannot efficiently learn anything about the
secret. The collection of "qualified" subsets is defined by a Boolean function.
It has been a major open problem to understand which (monotone) functions can
be realized by a computational secret-sharing schemes. Yao suggested a method
for secret-sharing for any function that has a polynomial-size monotone circuit
(a class which is strictly smaller than the class of monotone functions in P).
Around 1990 Rudich raised the possibility of obtaining secret-sharing for all
monotone functions in NP: In order to reconstruct the secret a set of parties
must be "qualified" and provide a witness attesting to this fact.
Recently, Garg et al. (STOC 2013) put forward the concept of witness
encryption, where the goal is to encrypt a message relative to a statement "x
in L" for a language L in NP such that anyone holding a witness to the
statement can decrypt the message, however, if x is not in L, then it is
computationally hard to decrypt. Garg et al. showed how to construct several
cryptographic primitives from witness encryption and gave a candidate
construction.
One can show that computational secret-sharing implies witness encryption for
the same language. Our main result is the converse: we give a construction of a
computational secret-sharing scheme for any monotone function in NP assuming
witness encryption for NP and one-way functions. As a consequence we get a
completeness theorem for secret-sharing: computational secret-sharing scheme
for any single monotone NP-complete function implies a computational
secret-sharing scheme for every monotone function in NP
Multilevel Threshold Secret and Function Sharing based on the Chinese Remainder Theorem
A recent work of Harn and Fuyou presents the first multilevel (disjunctive)
threshold secret sharing scheme based on the Chinese Remainder Theorem. In this
work, we first show that the proposed method is not secure and also fails to
work with a certain natural setting of the threshold values on compartments. We
then propose a secure scheme that works for all threshold settings. In this
scheme, we employ a refined version of Asmuth-Bloom secret sharing with a
special and generic Asmuth-Bloom sequence called the {\it anchor sequence}.
Based on this idea, we also propose the first multilevel conjunctive threshold
secret sharing scheme based on the Chinese Remainder Theorem. Lastly, we
discuss how the proposed schemes can be used for multilevel threshold function
sharing by employing it in a threshold RSA cryptosystem as an example
An ideal multi-secret sharing scheme based on minimal privileged coalitions
How to construct an ideal multi-secret sharing scheme for general access
structures is difficult. In this paper, we solve an open problem proposed by
Spiez et al.recently [Finite Fields and Their Application, 2011(17) 329-342],
namely to design an algorithm of privileged coalitions of any length if such
coalitions exist. Furthermore, in terms of privileged coalitions, we show that
most of the existing multi-secret sharing schemes based on Shamir threshold
secret sharing are not perfect by analyzing Yang et al.'s scheme and Pang et
al.'s scheme. Finally, based on the algorithm mentioned above, we devise an
ideal multi-secret sharing scheme for families of access structures, which
possesses more vivid authorized sets than that of the threshold scheme.Comment: 13page
Fourier-based Function Secret Sharing with General Access Structure
Function secret sharing (FSS) scheme is a mechanism that calculates a
function f(x) for x in {0,1}^n which is shared among p parties, by using
distributed functions f_i:{0,1}^n -> G, where G is an Abelian group, while the
function f:{0,1}^n -> G is kept secret to the parties. Ohsawa et al. in 2017
observed that any function f can be described as a linear combination of the
basis functions by regarding the function space as a vector space of dimension
2^n and gave new FSS schemes based on the Fourier basis. All existing FSS
schemes are of (p,p)-threshold type. That is, to compute f(x), we have to
collect f_i(x) for all the distributed functions. In this paper, as in the
secret sharing schemes, we consider FSS schemes with any general access
structure. To do this, we observe that Fourier-based FSS schemes by Ohsawa et
al. are compatible with linear secret sharing scheme. By incorporating the
techniques of linear secret sharing with any general access structure into the
Fourier-based FSS schemes, we show Fourier-based FSS schemes with any general
access structure.Comment: 12 page
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