11,327 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
On asymptotically good ramp secret sharing schemes
Asymptotically good sequences of linear ramp secret sharing schemes have been
intensively studied by Cramer et al. in terms of sequences of pairs of nested
algebraic geometric codes. In those works the focus is on full privacy and full
reconstruction. In this paper we analyze additional parameters describing the
asymptotic behavior of partial information leakage and possibly also partial
reconstruction giving a more complete picture of the access structure for
sequences of linear ramp secret sharing schemes. Our study involves a detailed
treatment of the (relative) generalized Hamming weights of the considered
codes
Nearly optimal robust secret sharing
Abstract: We prove that a known approach to improve Shamir's celebrated secret sharing scheme; i.e., adding an information-theoretic authentication tag to the secret, can make it robust for n parties against any collusion of size ÎŽn, for any constant ÎŽ â (0; 1/2). This result holds in the so-called ânonrushingâ model in which the n shares are submitted simultaneously for reconstruction. We thus finally obtain a simple, fully explicit, and robust secret sharing scheme in this model that is essentially optimal in all parameters including the share size which is k(1+o(1))+O(Îș), where k is the secret length and Îș is the security parameter. Like Shamir's scheme, in this modified scheme any set of more than ÎŽn honest parties can efficiently recover the secret. Using algebraic geometry codes instead of Reed-Solomon codes, the share length can be decreased to a constant (only depending on ÎŽ) while the number of shares n can grow independently. In this case, when n is large enough, the scheme satisfies the âthresholdâ requirement in an approximate sense; i.e., any set of ÎŽn(1 + Ï) honest parties, for arbitrarily small Ï > 0, can efficiently reconstruct the secret
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
Ideal Tightly Couple (t,m,n) Secret Sharing
As a fundamental cryptographic tool, (t,n)-threshold secret sharing
((t,n)-SS) divides a secret among n shareholders and requires at least t,
(t<=n), of them to reconstruct the secret. Ideal (t,n)-SSs are most desirable
in security and efficiency among basic (t,n)-SSs. However, an adversary, even
without any valid share, may mount Illegal Participant (IP) attack or
t/2-Private Channel Cracking (t/2-PCC) attack to obtain the secret in most
(t,n)-SSs.To secure ideal (t,n)-SSs against the 2 attacks, 1) the paper
introduces the notion of Ideal Tightly cOupled (t,m,n) Secret Sharing (or
(t,m,n)-ITOSS ) to thwart IP attack without Verifiable SS; (t,m,n)-ITOSS binds
all m, (m>=t), participants into a tightly coupled group and requires all
participants to be legal shareholders before recovering the secret. 2) As an
example, the paper presents a polynomial-based (t,m,n)-ITOSS scheme, in which
the proposed k-round Random Number Selection (RNS) guarantees that adversaries
have to crack at least symmetrical private channels among participants before
obtaining the secret. Therefore, k-round RNS enhances the robustness of
(t,m,n)-ITOSS against t/2-PCC attack to the utmost. 3) The paper finally
presents a generalized method of converting an ideal (t,n)-SS into a
(t,m,n)-ITOSS, which helps an ideal (t,n)-SS substantially improve the
robustness against the above 2 attacks
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
Quantum Stabilizer Codes Can Realize Access Structures Impossible by Classical Secret Sharing
We show a simple example of a secret sharing scheme encoding classical secret
to quantum shares that can realize an access structure impossible by classical
information processing with limitation on the size of each share. The example
is based on quantum stabilizer codes.Comment: LaTeX2e, 5 pages, no figure. Comments from readers are welcom
Improved Bounds on the Threshold Gap in Ramp Secret Sharing
ProducciĂłn CientĂficaAbstract: In this paper we consider linear secret sharing schemes over a finite field Fq, where the secret is a vector in Fâq and each of the n shares is a single element of Fq. We obtain lower bounds on the so-called threshold gap g of such schemes, defined as the quantity rât where r is the smallest number such that any subset of r shares uniquely determines the secret and t is the largest number such that any subset of t shares provides no information about the secret. Our main result establishes a family of bounds which are tighter than previously known bounds for ââ„2. Furthermore, we also provide bounds, in terms of n and q, on the partial reconstruction and privacy thresholds, a more fine-grained notion that considers the amount of information about the secret that can be contained in a set of shares of a given size. Finally, we compare our lower bounds with known upper bounds in the asymptotic setting.Danish Council for Independent Research (grant DFF-4002- 00367)Ministerio de EconomĂa, Industria y Competitividad (grants MTM2015-65764-C3-2-P / MTM2015-69138- REDT)RYC-2016-20208 (AEI/FSE/UE)Junta de Castilla y LeĂłn (grant VA166G18
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