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An algebraic approach for decoding spread codes
On the relationship between the traceability properties of Reed-Solomon codes
1. | Department of Telematics Engineering, Universitat Politècnica de Catalunya, C. Jordi Girona 1-3, 08034 Barcelona, Spain, Spain |
2. | Department of Telematics Engineering, Universitat Politècnica de Catalunya, C. Jordi Girona 1-3, 08034 Barcelona, Spain, and Centre Tecnològic de Telecomunicacions de Catalunya (CTTC), Av. Carl Friedrich Gauss 7, 08860 Castelldefels (Barcelona), Spain |
References:
[1] |
A. Barg, G. R. Blakley and G. A. Kabatiansky, Digital fingerprinting codes: problem statements, constructions, identification of traitors,, IEEE Trans. Inform. Theory, 49 (2003), 852.
doi: 10.1109/TIT.2003.809570. |
[2] |
D. Boneh and J. Shaw, Collusion-secure fingerprinting for digital data,, in, (1995), 452.
doi: 10.1007/3-540-44750-4_36. |
[3] |
D. Boneh and J. Shaw, Collusion-secure fingerprinting for digital data,, IEEE Trans. Inform. Theory, 44 (1998), 1897.
doi: 10.1109/18.705568. |
[4] |
B. Chor, A. Fiat and M. Naor, Tracing traitors,, in, (1994), 480. Google Scholar |
[5] |
B. Chor, A. Fiat, M. Naor and B. Pinkas, Tracing traitors,, IEEE Trans. Inform. Theory, 46 (2000), 893.
doi: 10.1109/18.841169. |
[6] |
G. D. Cohen and H. G. Schaathun, Asymptotic overview on separating codes,, Tech. Report 248, (2003). Google Scholar |
[7] |
G. D. Cohen and H. G. Schaathun, Upper bounds on separating codes,, IEEE Trans. Inform. Theory, 50 (2004), 1291.
doi: 10.1109/TIT.2004.828140. |
[8] |
M. Fernandez, J. Cotrina, M. Soriano and N. Domingo, A note about the identifier parent property in Reed-Solomon codes,, Comput. Security, 29 (2010), 628.
doi: 10.1016/j.cose.2009.12.012. |
[9] |
A. D. Friedman, R. L. Graham and J. D. Ullman, Universal single transition time asynchronous state assignments,, IEEE Trans. Comput., C-18 (1969), 541.
doi: 10.1109/T-C.1969.222707. |
[10] |
H. D. L. Hollmann, J. H. van Lint, J.-P. Linnartz and L. M. G. M. Tolhuizen, On codes with the identifiable parent property,, J. Combin. Theory Ser. A, 82 (1998), 121.
doi: 10.1006/jcta.1997.2851. |
[11] |
H. Jin and M. Blaum, Combinatorial properties for traceability codes using error correcting codes,, IEEE Trans. Inform. Theory, 53 (2007), 804.
doi: 10.1109/TIT.2006.889730. |
[12] |
J. Körner and G. Simonyi, Separating partition systems and locally different sequences,, SIAM J. Discr. Math., 1 (1988), 355.
doi: 10.1137/0401035. |
[13] |
R. Lidl and H. Niederreiter, "Introduction to Finite Fields and their Applications,'' revised edition,, Cambridge University Press, (1994).
doi: 10.1017/CBO9781139172769. |
[14] |
M. S. Pinsker and Y. L. Sagalovich, Lower bound on the cardinality of code of automata's states,, Probl. Inform. Transm., 8 (1972), 59. Google Scholar |
[15] |
I. S. Reed and G. Solomon, Polynomial codes over certain finite fields,, SIAM J. Appl. Math., 8 (1960), 300.
doi: 10.1137/0108018. |
[16] |
Y. L. Sagalovich, Completely separating systems,, Probl. Inform. Transm., 18 (1982), 140.
|
[17] |
Y. L. Sagalovich, Separating systems,, Probl. Inform. Transm., 30 (1994), 105.
|
[18] |
A. Silverberg, J. Staddon and J. L. Walker, Efficient traitor tracing algorithms using list decoding,, in, (2001), 175.
doi: 10.1007/3-540-45682-1_11. |
[19] |
A. Silverberg, J. Staddon and J. L. Walker, Applications of list decoding to tracing traitors,, IEEE Trans. Inform. Theory, 49 (2003), 1312.
doi: 10.1109/TIT.2003.810630. |
[20] |
J. N. Staddon, D. R. Stinson and R. Wei, Combinatorial properties of frameproof and traceability codes,, IEEE Trans. Inform. Theory, 47 (2001), 1042.
doi: 10.1109/18.915661. |
[21] |
D. R. Stinson, T. van Trung and R. Wei, Secure frameproof codes, key distribution patterns, group testing algorithms and related structures,, J. Stat. Plan. Infer., 86 (2000), 595.
doi: 10.1016/S0378-3758(99)00131-7. |
show all references
References:
[1] |
A. Barg, G. R. Blakley and G. A. Kabatiansky, Digital fingerprinting codes: problem statements, constructions, identification of traitors,, IEEE Trans. Inform. Theory, 49 (2003), 852.
doi: 10.1109/TIT.2003.809570. |
[2] |
D. Boneh and J. Shaw, Collusion-secure fingerprinting for digital data,, in, (1995), 452.
doi: 10.1007/3-540-44750-4_36. |
[3] |
D. Boneh and J. Shaw, Collusion-secure fingerprinting for digital data,, IEEE Trans. Inform. Theory, 44 (1998), 1897.
doi: 10.1109/18.705568. |
[4] |
B. Chor, A. Fiat and M. Naor, Tracing traitors,, in, (1994), 480. Google Scholar |
[5] |
B. Chor, A. Fiat, M. Naor and B. Pinkas, Tracing traitors,, IEEE Trans. Inform. Theory, 46 (2000), 893.
doi: 10.1109/18.841169. |
[6] |
G. D. Cohen and H. G. Schaathun, Asymptotic overview on separating codes,, Tech. Report 248, (2003). Google Scholar |
[7] |
G. D. Cohen and H. G. Schaathun, Upper bounds on separating codes,, IEEE Trans. Inform. Theory, 50 (2004), 1291.
doi: 10.1109/TIT.2004.828140. |
[8] |
M. Fernandez, J. Cotrina, M. Soriano and N. Domingo, A note about the identifier parent property in Reed-Solomon codes,, Comput. Security, 29 (2010), 628.
doi: 10.1016/j.cose.2009.12.012. |
[9] |
A. D. Friedman, R. L. Graham and J. D. Ullman, Universal single transition time asynchronous state assignments,, IEEE Trans. Comput., C-18 (1969), 541.
doi: 10.1109/T-C.1969.222707. |
[10] |
H. D. L. Hollmann, J. H. van Lint, J.-P. Linnartz and L. M. G. M. Tolhuizen, On codes with the identifiable parent property,, J. Combin. Theory Ser. A, 82 (1998), 121.
doi: 10.1006/jcta.1997.2851. |
[11] |
H. Jin and M. Blaum, Combinatorial properties for traceability codes using error correcting codes,, IEEE Trans. Inform. Theory, 53 (2007), 804.
doi: 10.1109/TIT.2006.889730. |
[12] |
J. Körner and G. Simonyi, Separating partition systems and locally different sequences,, SIAM J. Discr. Math., 1 (1988), 355.
doi: 10.1137/0401035. |
[13] |
R. Lidl and H. Niederreiter, "Introduction to Finite Fields and their Applications,'' revised edition,, Cambridge University Press, (1994).
doi: 10.1017/CBO9781139172769. |
[14] |
M. S. Pinsker and Y. L. Sagalovich, Lower bound on the cardinality of code of automata's states,, Probl. Inform. Transm., 8 (1972), 59. Google Scholar |
[15] |
I. S. Reed and G. Solomon, Polynomial codes over certain finite fields,, SIAM J. Appl. Math., 8 (1960), 300.
doi: 10.1137/0108018. |
[16] |
Y. L. Sagalovich, Completely separating systems,, Probl. Inform. Transm., 18 (1982), 140.
|
[17] |
Y. L. Sagalovich, Separating systems,, Probl. Inform. Transm., 30 (1994), 105.
|
[18] |
A. Silverberg, J. Staddon and J. L. Walker, Efficient traitor tracing algorithms using list decoding,, in, (2001), 175.
doi: 10.1007/3-540-45682-1_11. |
[19] |
A. Silverberg, J. Staddon and J. L. Walker, Applications of list decoding to tracing traitors,, IEEE Trans. Inform. Theory, 49 (2003), 1312.
doi: 10.1109/TIT.2003.810630. |
[20] |
J. N. Staddon, D. R. Stinson and R. Wei, Combinatorial properties of frameproof and traceability codes,, IEEE Trans. Inform. Theory, 47 (2001), 1042.
doi: 10.1109/18.915661. |
[21] |
D. R. Stinson, T. van Trung and R. Wei, Secure frameproof codes, key distribution patterns, group testing algorithms and related structures,, J. Stat. Plan. Infer., 86 (2000), 595.
doi: 10.1016/S0378-3758(99)00131-7. |
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