Explicit Construction of Secure Frameproof Codes

Dongvu Tonien; Reihaneh Safavi-Naini

Paper 2005/275

Explicit Construction of Secure Frameproof Codes

Dongvu Tonien and Reihaneh Safavi-Naini

Abstract

$Γ$ 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 $Γ$ if at each position $i$ , $1 \leq i \leq L$ , $w$ inherits a symbol from one of its parents, that is $w_{i} \in {w_{i}^{(1)}, w_{i}^{(2)}, \dots, w_{i}^{(t)}}$ . 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 -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.

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.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. International Journal of Pure and Applied Mathematics, Volume 6, No. 3, 2003, 343-360
Keywords: combinatorial cryptography fingerprinting codes secure frameproof codes traitor tracing
Contact author(s): dong @ uow edu au
History: 2005-08-17: revised; 2005-08-17: received; See all versions
Short URL: https://ia.cr/2005/275
License: CC BY

BibTeX

@misc{cryptoeprint:2005/275,
      author = {Dongvu Tonien and Reihaneh Safavi-Naini},
      title = {Explicit Construction of Secure Frameproof Codes},
      howpublished = {Cryptology {ePrint} Archive, Paper 2005/275},
      year = {2005},
      url = {https://eprint.iacr.org/2005/275}
}