**Explicit Construction of Secure Frameproof Codes**

*Dongvu Tonien and 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.

**Category / Keywords: **combinatorial cryptography, fingerprinting codes, secure frameproof codes, traitor tracing

**Publication Info: **International Journal of Pure and Applied Mathematics, Volume 6, No. 3, 2003, 343-360

**Date: **received 16 Aug 2005, last revised 17 Aug 2005

**Contact author: **dong at uow edu au

**Available format(s): **PDF | BibTeX Citation

**Note: **This is the revised version of the paper published in International Journal of Pure and Applied Mathematics, volume 6 no. 3, 2003, 343-360.

**Version: **20050817:232701 (All versions of this report)

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