On Some Methods for Unconditionally Secure Key Distributionand Broadcast Encryption
Designs, Codes and Cryptography - Special issue: selected areas in cryptography I
On codes with the identifiable parent property
Journal of Combinatorial Theory Series A
Explicit constructions of perfect hash families from algebraic curves over finite fields
Journal of Combinatorial Theory Series A
Rational Points on Curves over Finite Fields: Theory and Applications
Rational Points on Curves over Finite Fields: Theory and Applications
Algebraic-Geometric Codes
A Hypergraph Approach to the Identifying Parent Property: The Case of Multiple Parents
SIAM Journal on Discrete Mathematics
INDOCRYPT '01 Proceedings of the Second International Conference on Cryptology in India: Progress in Cryptology
The Lovász Local Lemma and Its Applications to some Combinatorial Arrays
Designs, Codes and Cryptography
New Constructions for IPP Codes
Designs, Codes and Cryptography
Combinatorial properties of frameproof and traceability codes
IEEE Transactions on Information Theory
Testers and their applications
Proceedings of the 5th conference on Innovations in theoretical computer science
Randomized post-optimization for t-restrictions
Information Theory, Combinatorics, and Search Theory
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Let X be a set of order n and Y be a set of order m. An (n,m,{w 1, w 2})-separating hash family is a set $$\mathcal {F}$$ of N functions from X to Y such that for any $$X_1, X_2 \subseteq X$$ with $$X_1\cap X_2=\emptyset$$ , |X 1| = w 1 and |X 2| = w 2, there exists an element $$f\in \mathcal {F}$$ such that $$f(X_1)\cap f(X_2)=\emptyset$$ . In this paper, we provide explicit constructions of separating hash families using algebraic curves over finite fields. In particular, applying the Garcia---Stichtenoth curves, we obtain an infinite class of explicitly constructed (n,m,{w 1,w 2})---separating hash families with $$N=\mathcal {O}(\log\,n)$$ for fixed m, w 1, and w 2. Similar results for strong separating hash families are also obtained. As consequences of our main results, we present explicit constructions of infinite classes of frameproof codes, secure frameproof codes and identifiable parent property codes with length $$N=\mathcal {O}(\log\,n)$$ where n is the size of the codes. In fact, all the above explicit constructions of hash families and codes provide the best asymptotic behavior achieving the bound $$N=\mathcal {O}(\log\,n)$$ , which substantially improve the results in [ 8, 15, 17] give an answer to the fifth open problem presented in [11].