Some recursive constructions for perfect hash families

Atıcı, Mustafa; Magliveras, Spyros S.; Stinson, D. R.; Wen, Wei

doi:10.1002/(sici)1520-6610(1996)4:5<353::aid-jcd4>3.3.co;2-6

Cited by 12 publications

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“…Our interest in this paper is in ®nding explicit constructions for perfect hash families using combinatorial techniques. We generalize and improve several results from Atici, Magliveras, Stinson, and Wei [3]. In particular, we present several easy methods of constructing perfect hash families from orthogonal arrays and related structures.…”

Section: Introductionmentioning

confidence: 68%

New constructions for perfect hash families and related structures using combinatorial designs and codes

Stinson

Wei

Zhu³

2000

J. Combin. Designs

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107

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In this paper, we consider explicit constructions of perfect hash families using combinatorial methods. We provide several direct constructions from combinatorial structures related to orthogonal arrays. We also simplify and generalize a recursive construction due to Atici, Magliversas, Stinson and Wei [3]. Using similar methods, we also obtain efficient constructions for separating hash families which result in improved existence results for structures such as separating systems, key distribution patterns, group testing algorithms, cover‐free families and secure frameproof codes. © 2000 John Wiley & Sons, Inc. J Combin Designs 8:189–200, 2000

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Section: Introductionmentioning

confidence: 68%

New constructions for perfect hash families and related structures using combinatorial designs and codes

Stinson

Wei

Zhu³

2000

J. Combin. Designs

Self Cite

107

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“…If there exist ( t 2 ) − 1 MOLS of order k and a PHF(N 0 ; k, v, t), then there exists a PHF((( t 2 ) + 1)N 0 ; k 2 , v, t). Theorem 4.2 is equivalent to Theorem 13 in [31]; it generalizes and improves upon two constructions given in [4]. Theorem 4.2 is equivalent to Theorem 13 in [31]; it generalizes and improves upon two constructions given in [4].…”

Section: Recursive Constructionsmentioning

confidence: 80%

“…Finally, Atici et al [4] provide a construction from resolvable balanced incomplete block designs (RBIBDs):…”

Section: Known Direct Constructionsmentioning

confidence: 99%

Perfect Hash Families: Constructions and Existence

Walker¹,

Colbourn²

2007

Journal of Mathematical Cryptology

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A perfect hash family PHF(N ; k, v, t) is an N × k array on v symbols with v ≥ t, in which in every N × t subarray, at least one row is comprised of distinct symbols. Perfect hash families have a wide range of applications in cryptography, particularly to secure frameproof codes, in database management, and indirectly in software interaction testing. New recursive constructions, new direct constructions, and PHFs found using tabu search are provided here. The first general tables of the best known sizes of PHFs are presented; in the process, the known direct and recursive constructions are surveyed.An m × n latin rectangle is an m × n array, m ≤ n, in which each cell contains a symbol from an n-set; no symbol occurs twice in any row or in any column. Two m×n latin rectangles are orthogonal if, when superimposed, every ordered pair of symbols arises at most once. A set of k latin rectangles, each m × n, is mutually orthogonal if every two latin rectangles in the set is orthogonal; such a set is called k MOLR. An equivalent structure, an "(n; m, k + 2)-difference function family", is defined in [31]. When m = n, this is the more standard combinatorial structure, mutually orthogonal latin squares, or MOLS.Theorem 2.8 ([29]). Suppose there are at least s = ( t 2 ) − 1 MOLR of size m × n. Then there exists a PHF(s + 2; mn, n, t).Corollary 2.9 ([29]). Suppose there are at least s = ( t 2 ) − 1 MOLS of order v. Then there exists a PHF(s + 2; v 2 , v, t).

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“…(f (n) = Θ(log n) means that there exist constants c 1 , c 2 and n 0 such that for n > n 0 , c 1 log n ≤ f (n) ≤ c 2 log n.) In [1,5] some constructions with reasonable asymptotic performance are given. For example, for fixed m and w, N is a polynomial function of log n. Various other bounds on N (n, m, w) can be found in [15,1,7,3].…”

Section: Theorem 4 Suppose There Exists a Cartesianmentioning

confidence: 99%

“…For example, for fixed m and w, N is a polynomial function of log n. Various other bounds on N (n, m, w) can be found in [15,1,7,3].…”

Section: Theorem 4 Suppose There Exists a Cartesianmentioning

confidence: 99%

Broadcast Authentication in Group Communication

Wang

1999

Advances in Cryptology - ASIACRYPT’99

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Abstract. Traditional point-to-point message authentication systems have been extensively studied in the literature. In this paper we consider authentication for group communication. The basic primitive is a multireceiver authentication system with dynamic sender (DMRA-code). In a DMRA-code any member of a group can broadcast an authenticated message such that all other group members can individually verify its authenticity. In this paper first we give a new and flexible 'synthesis' construction for DMRA-codes by combining an authentication code (Acode) and a key distribution pattern. Next we extend DMRA-codes to tDMRA-codes in which t senders are allowed. We give two constructions for tDMRA-codes, one algebraic and one by 'synthesis' of an A-code and a perfect hash family. To demonstrate the usefulness of DMRA systems, we modify a secure dynamic conference key distribution system to construct a key-efficient secure dynamic conference system that provides secrecy and authenticity for communication among conferencees. The system is key-efficient because the key requirement is essentially the same as the original conference key distribution system and so authentication is effectively obtained without any extra cost. We show universality of 'synthesis' constructions for unconditional and computational security model that suggests direct application of our results to real-life multicasting scenarios in computer networks. We discuss possible extensions to this work.

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Some recursive constructions for perfect hash families

Cited by 12 publications

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New constructions for perfect hash families and related structures using combinatorial designs and codes

New constructions for perfect hash families and related structures using combinatorial designs and codes

Perfect Hash Families: Constructions and Existence

Broadcast Authentication in Group Communication

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