New combinatorial designs and their applications to authentication codes and secret sharing schemes

Ogata, Wakaha; Kurosawa, Kaoru; Stinson, Douglas R.; Saido, Hajime

doi:10.1016/s0012-365x(03)00283-8

Cited by 79 publications

(114 citation statements)

References 12 publications

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“…In a difference family of sets, each nonidentity element of a group will arise some fixed number of times as a difference between same-set elements. External difference families (EDFs) were introduced in [14] as a method of constructing optimal robust secret sharing schemes. In an EDF, as the name suggests, each nonidentity element arises a fixed number of times as a difference between elements in distinct sets.…”

Section: Introductionmentioning

confidence: 99%

Near-complete external difference families

Davis

Huczynska

Mullen

2016

Des. Codes Cryptogr.

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We introduce and explore near-complete external difference families, a partitioning of the nonidentity elements of a group so that each nonidentity element is expressible as a difference of elements from distinct subsets a fixed number of times. We show that the existence of such an object implies the existence of a near-resolvable design. We provide examples and general constructions of these objects, some of which lead to new parameter families of near-resolvable designs on a non-prime-power number of points. Our constructions employ cyclotomy, partial difference sets, and Galois Rings.AMS classification: 94C30 51E20 94A62 05B10

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Section: Introductionmentioning

confidence: 99%

Near-complete external difference families

Davis

Huczynska

Mullen

2016

Des. Codes Cryptogr.

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“…Although AMD codes were never formally defined in previous work, some constructions of AMD codes have appeared, mostly in connection with making secret sharing robust [20,7,21]. Although some of these constructions are essentially optimal, all of them are largely inflexible in that the error probability δ is dictated by the cardinality of the source space S: δ ≈ 1/|S|.…”

Section: Linear Secret Sharing Schemesmentioning

confidence: 99%

“…Our combinatorial approach must be discussed with respect to earlier work by Ogata and Kurosawa [20] and Ogata, Kurosawa, Stinson and Saido [21]. In [20] the idea of using the classical notion of planar difference sets is introduced, and applications to (in our terminology) weakly secure AMD codes are given.…”

Section: C3 Relation To Earlier Workmentioning

confidence: 99%

“…The tag size equals ̟ = log(q 2 + q + 1) − log(q + 1), which lies between log(q) and log(q + 1). See also [21] for a more general approach. As before, the error probability is determined by the source space and hence the approach is not flexible.…”

Section: C3 Relation To Earlier Workmentioning

confidence: 99%

“…Motivated by this, the above approach is extended in [21] to using external difference families (EDF), as introduced there. A (G, c, λ) S-EDF consists consists of a group G of order G and S disjoint non-empty subsets V 1 , .…”

Section: C3 Relation To Earlier Workmentioning

confidence: 99%

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Detection of Algebraic Manipulation with Applications to Robust Secret Sharing and Fuzzy Extractors

Cramer

Dodis

Fehr

et al.

Advances in Cryptology – EUROCRYPT 2008

219

224

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Abstract.Consider an abstract storage device Σ(G) that can hold a single element x from a fixed, publicly known finite group G. Storage is private in the sense that an adversary does not have read access to Σ(G) at all. However, Σ(G) is non-robust in the sense that the adversary can modify its contents by adding some offset ∆ ∈ G. Due to the privacy of the storage device, the value ∆ can only depend on an adversary's a priori knowledge of x. We introduce a new primitive called an algebraic manipulation detection (AMD) code, which encodes a source s into a value x stored on Σ(G) so that any tampering by an adversary will be detected, except with a small error probability δ. We give a nearly optimal construction of AMD codes, which can flexibly accommodate arbitrary choices for the length of the source s and security level δ. We use this construction in two applications:-We show how to efficiently convert any linear secret sharing scheme into a robust secret sharing scheme, which ensures that no unqualified subset of players can modify their shares and cause the reconstruction of some value s ′ = s. -We show how how to build nearly optimal robust fuzzy extractors for several natural metrics. Robust fuzzy extractors enable one to reliably extract and later recover random keys from noisy and non-uniform secrets, such as biometrics, by relying only on non-robust public storage. In the past, such constructions were known only in the random oracle model, or required the entropy rate of the secret to be greater than half. Our construction relies on a randomly chosen common reference string (CRS) available to all parties.

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Splitting balanced incomplete block designs with block size 3 × 2

Du¹

2004

J of Combinatorial Designs

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Splitting balanced incomplete block designs were first formulated by Ogata, Kurosawa, Stinson, and Saido recently in the investigation of authentication codes. This article investigates the existence of splitting balanced incomplete block designs, i.e., ðv v; 3k; Þ-splitting BIBDs; we give the spectrum of ðv v; 3 Â 2; Þ-splitting BIBDs. As an application, we obtain an infinite class of 2-splitting A-codes. #

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New combinatorial designs and their applications to authentication codes and secret sharing schemes

Cited by 79 publications

References 12 publications

Near-complete external difference families

Near-complete external difference families

Detection of Algebraic Manipulation with Applications to Robust Secret Sharing and Fuzzy Extractors

Splitting balanced incomplete block designs with block size 3 × 2

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