IJPAM: Volume 6, No. 3 (2003)


Vu Dong D. Tô$^1$, R. Safavi-Naini$^2$
School of Information Technology and Computer Science
University of Wollongong
$^1$e-mail: dong@uow.edu.au
$^2$e-mail: rei@uow.edu.au

Abstract.$\Gamma$ is a $q$-ary code of length $L$. A word $w$ is called a descendant of a coalition of codewords $w^{(1)}$, $w^{(2)}$, ..., $w^{(t)}$ 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 Staddon et al [#!SSW00!#] 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 Tô et al [#!TSW02!#]. The length of our new code is logarithmically small compared to its size.

Received: March 13, 2003

AMS Subject Classification: 68R05, 94A60, 05B99

Key Words and Phrases: secure frameproof codes, fingerprinting codes, traceability codes

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2003
Volume: 6
Issue: 3