Welcome to the resource topic for 2005/275
Title:
Explicit Construction of Secure Frameproof Codes
Authors: Dongvu Tonien, Reihaneh Safavi-Naini
Abstract:\Gamma is a q-ary code of length L. A word w is called a descendant of a coalition of codewords w^{(1)}, w^{(2)}, \dots, w^{(t)} of \Gamma if at each position i, 1 \leq i \leq L, w inherits a symbol from one of its parents, that is w_i \in \{ w^{(1)}_i, w^{(2)}_i, \dots, w^{(t)}_i \}. A k-secure frameproof code (k-SFPC) ensures that any two disjoint coalitions of size at most k have no common descendant. Several probabilistic methods prove the existance of codes but there are not many explicit constructions. Indeed, it is an open problem in [J. Staddon et al.,
IEEE Trans. on Information Theory, 47 (2001), pp. 1042–1049] to construct explicitly q-ary 2-secure frameproof code for arbitrary q.
In this paper, we present several explicit constructions of q-ary 2-SFPCs. These constructions are generalisation of the binary inner code of the secure code in [V.D. To et al., Proceeding of IndoCrypt’02, LNCS 2551, pp. 149–162, 2002]. The length of our new code is logarithmically small compared to its size.
ePrint: https://eprint.iacr.org/2005/275
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