13,093 research outputs found
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
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
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
A simple combinatorial treatment of constructions and threshold gaps of ramp schemes
We give easy proofs of some recent results concerning threshold gaps in ramp schemes. We then generalise a construction method for ramp schemes employing error-correcting codes so that it can be applied using nonlinear (as well as linear) codes. Finally, as an immediate consequence of these results, we provide a new explicit bound on the minimum length of a code having a specified distance and dual distance
Still Wrong Use of Pairings in Cryptography
Several pairing-based cryptographic protocols are recently proposed with a
wide variety of new novel applications including the ones in emerging
technologies like cloud computing, internet of things (IoT), e-health systems
and wearable technologies. There have been however a wide range of incorrect
use of these primitives. The paper of Galbraith, Paterson, and Smart (2006)
pointed out most of the issues related to the incorrect use of pairing-based
cryptography. However, we noticed that some recently proposed applications
still do not use these primitives correctly. This leads to unrealizable,
insecure or too inefficient designs of pairing-based protocols. We observed
that one reason is not being aware of the recent advancements on solving the
discrete logarithm problems in some groups. The main purpose of this article is
to give an understandable, informative, and the most up-to-date criteria for
the correct use of pairing-based cryptography. We thereby deliberately avoid
most of the technical details and rather give special emphasis on the
importance of the correct use of bilinear maps by realizing secure
cryptographic protocols. We list a collection of some recent papers having
wrong security assumptions or realizability/efficiency issues. Finally, we give
a compact and an up-to-date recipe of the correct use of pairings.Comment: 25 page
Algebraic Geometric Secret Sharing Schemes over Large Fields Are Asymptotically Threshold
In Chen-Cramer Crypto 2006 paper \cite{cc} algebraic geometric secret sharing
schemes were proposed such that the "Fundamental Theorem in
Information-Theoretically Secure Multiparty Computation" by Ben-Or, Goldwasser
and Wigderson \cite{BGW88} and Chaum, Cr\'{e}peau and Damg{\aa}rd \cite{CCD88}
can be established over constant-size base finite fields. These algebraic
geometric secret sharing schemes defined by a curve of genus over a
constant size finite field is quasi-threshold in the following
sense, any subset of players (non qualified) has no information of
the secret and any subset of players (qualified) can reconstruct
the secret. It is natural to ask that how far from the threshold these
quasi-threshold secret sharing schemes are? How many subsets of players can recover the secret or have no information of the secret?
In this paper it is proved that almost all subsets of
players have no information of the secret and almost all subsets of players can reconstruct the secret when the size goes to the
infinity and the genus satisfies . Then algebraic
geometric secret sharing schemes over large finite fields are asymptotically
threshold in this case. We also analyze the case when the size of the base
field is fixed and the genus goes to the infinity
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