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WoS  JIF 2026 : 0.4 (Q4)

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Open Access Research Article

Understanding traceable codes : A review of their functionality and importance

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pp. 793–810Vol. 47Issue 2February 2026DOI: 10.47974/JIOS-2187XML
Received:
08 Jul 2025
Published Online:
31 Jan 2026
Article type:
Research Article
Language:
EN
Article no.:
JIOS-2187
Pages:
793–810

Abstract

Traceable Codes and Frameproof Codes are Essential in Secure Communication, Data distribution, and copyright protection. These Combinatorial Codes enable the detection and prevention of malicious activities such as unauthorized redistribution and collusion. This paper reviews the foundational principles, significant developments, and practical applications of these codes. A Comparative Analysis of these codes highlight the Advancements in Construction Methods and identifies challenges and offers future Research directions.

Keywords

Subject Classifications

12F0512F0612F15

References

[1] A Barg, R Blakley and G Kabatiansky, “Digital Fingerprinting Codes: Problem Statements, Construction, identification of Traitors” IEEE Transactions on Information Theory, vol. 49. no. 4, pp. 852-865 (April 03).
[2] A. Barg and G. Kabatiansky, “A class of IPP Codes with efficient identification” J. Complexity, vol. 20, no. 23, pp. 35-39 (April 04).
[3] A. Barg, G. Cohen, S. Encheva, G. Kabatiansky and G. Zemor “A Hypergraph Approach to the Identifying Parent Property: The Case of Multiple Parents”  SIAM Journal of Discrete Mathematics (SIAM J. Discrete Math.), vol. 14,  pp. 423-431 (2001).
[4] Anu Kathuria, S.K. Arora, and Sudhir Batra, “On traceability property of equidistant codes” Journal of Discrete Mathematics, vol. 340, pp. 713-721 (2017).
[5] Anu Kathuria,  Sudhir Batra and S.K. Arora “A class of 2-FP Codes” Journal of Information and Optimization Sciences, Taylor and Francis, vol. 38, no. 8, pp.1311-1324 (December 2017) .
[6] Anu Kathuria and Sudhir Batra “On Algebraic Conditions of Equidistant Codes” International Journal of Science and Research Archive”, vol.8(02), pg. 575-588 (April 2023).
[7] L.R. Virmani, “The Theory of Error Correcting Codes”, Chapman and Hall, CRC Press
[8] B. Chor, A. Fiat and M. Naor, “Tracing Traitors”, in Advances in Cryptology – CRYPTO, 94 ( Lecture Notes in Computer Science) Berlin, Germany, Springer Verlag, vol. 839,  pp. 257-270 (1994). 
[9] B. Chor, A. Fiat and M. Naor, “Tracing Traitors”, IEEE Transactions on Information Theory, vol. 46, no. 3, pp. 893-910 (May 2000)
[10] B. Chor, A. Fiat and M. Naor, “Tracing Traitors”, in Advances in Cryptology – CRYPTO, 94 ( Lecture Notes in Computer Science) Berlin, Heidelberg, Springer NewYork, vol. 839,  pp. 480- 491 (1994). 
[11] Blackburn, Tuvi Etzion and Siaw – Ng. “Traceability Codes–Journal of Combinatorial Theory, https://doi.org/10.1016/j.jcta.2010.02.009
[12] D. Boneh and J. Shaw, “Collusion –Secure fingerprinting for Digital Data”, IEEE  Transactions on Information Theory,  vol. 44, pp. 1897-1905 (1998).
[13] D. Boneh and J. Shaw, “Collusion –Secure fingerprinting for Digital Data”, In Advances in Cryptology – CRYPTO ’95, (Lecture Notes in Computer Science), vol. 963, pp. 453-465, New York (1995).  
[14] D.R. Stinson, “Combinatorial Designs : Construction and Analysis”, Springer –Verlag, New York Berlin, Heidelberg (2003).   
[15] D.R.Stinson and R. Wei “Combinatorial Properties and Constructions of traceability schemes and frameproof codes”, SIAM Journal of Discrete Mathematics, vol.2, pp.41-53 (1998). 
[16] D.R. Stinson, Van Trung and  R.Wei “Secure frameproof Codes, Key Distribution Patterns, Group Testing Algorithms and related Structures”, Journal of Statistical Planning Inference, vol. 86(2), pp. 595-617 (2000).
[17] E.Rodriguez-Lois and Perez-Gonzalez, “Towards Traitor Tracing in Black-and-White-BoxDNN Watermarking with Tardos-based Codes, https://doi.org/10.1109/WIFS58808.2023.10374879
[18] Gerard Cohen and Encheva Sylvia “Frameproof Codes against coalition of pirates” Theoretical Computer Science, vol. 273, no. 2, pp.295-304 (February 2002).
[19] Gerard Cohen and Encheva Sylvia, “Some new p-array two secure frameproof codes” Applied Mathematics Letters, 14; pp.177-182 (2001).
[20] Ge, Shangguan, “Good Traceability Codes do exist” “https://doi.org/10.48550/arXiv.1601.04810
[21] Fang-Wei Fu,  Torleiv Klove and Yuan Luo “On Equidistant Constant Weight Codes” Discrete Applied Mathematics, 128, pg. 157-164 (2003). 
[22] H.D.L. Hollman, Jack H. Van Lint and Jean-Paul Linnartz “On codes with  the identifiable Parent Property” Journal of Combinatorial Theory, Series A-82, pp. 121-133 (1998).
[23] Hongxia Jin and Mario Blaum, “Combinatorial Properties of Traceability Codes using Error Correcting Codes” IEEE Transactions on Information Theory, vol. 53, no. 2 (February 2007).
[24] J.N. Staddon, D.R. Stinson and R. Wei, “Combinatorial Properties of Frameproof and  Traceable Codes” IEEE Transactions on Information Theory,  vol.47, pp. 1042-1049 (2001).
[25] J. Lofvenberg, “Binary Fingerprinting Codes” Designs Codes and Cryptography, vol. 36, pp. 69-81 (July 05).
[26] J. Moreira, M. Fernandez and M.Soriano “Properties and Evaluation of Fingerprinting Codes”, PHD. Thesis (2007) 
[27] K.Sinha, Z. Wang and D.Wu “Good Equidistant Codes constructed from Combinatorial Designs”, Discrete Mathematics, vol. 308, pp. 4205-4211 (2008).
[28] T. Lindkvist, “Fingerprinting of Digital Documents” Dissertation 706, Linkoping University, Sweden (2001).
[29] T. Lindkvist and J. Lofvenberg, and M. Svanstrom, “A class of traceability Codes” IEEE Transactions on Information Theory, vol. 48, 7, pp. 2094-2096 (2002).
[30] M. Fernandez and M. Soriano “Fingerprinting concatenated codes with efficient identification “Proc. ISC 02, Springer Publishing, Heidelberg, New York, pp. 459-470 (2002)
[31] M. Fernandez and M. Soriano, “Algorithm to decode Identifiable Parent Property Codes “Electronic Letters, 6th June, vol. 38, no. 12 (2002)
[32] M. Fernandez and M. Soriano,” On the IPP property of Reed Solomon Codes “in  Emerging Challenges for Security, Privacy and Trust, Advances in Information and Communication Technology vol. 297, Springer Boston, pp.87-97 2009.
[33] M. Fernandez and M. Soriano “A new class of IPP Codes for Fingerprinting Schemes “Springer –Verlag Berlin Heidelberg, pp. 398-409 (2005).
[34] M. Fernandez and Josep Cotrina “Equidistant Binary Fingerprinting Codes : Existence and Identification Algorithms”, Proc. Springer –Verlag, Berlin Heidelberg, pp. 527-536 (2005).
[35] M. Fernandez and Josep Cotrina “A note about the Traceability of Linear Codes”, Springer – Verlag Berlin, Heidelberg, pp. 308-409 (2005).
[36] F. J. Mac Williams and N. J. A. Sloane, “The Theory of Error Correcting Codes” Bell Laboratories, Murray Hills, NJO 7974, USA (1978).
[37] Marco Dalai and Stefano Della Fiore “Bounds and Algorithms for Frameproof Codes And related Combinatorial Structures” IEEE Transactions on Information  Theory, 713-721 (2023)
[38] Miao Liu and Ching Shangguan “Near Optimal Constructions of frameproof codes” IEEE International Symposium on Information Theory (2024), https://doi.org/10.1109/ISIT57864.2024.10619230.
[39] N.Wagner, “Fingerprinting Techniques “in Proceedings 1983, IEEE Symposium on Security and Privacy, pp.18-22 (April 1983).
[40] Olivier Billet and Duong Phan “Efficient Traitor Tracing from Collusion Secure Codes, Springer Nature, Information Theoretic Securitry (2008)”. 
[41] R. Safavi –Naini and Yeing Want “New Results on Frameproof Codes and Traceability Schemes” Proc. Wollongong, pp. 3029-3033 (2001).
[42] R.S.Veerubhotla, V.P.Gualti and A. K.Pujari “Gossip Codes for Fingerprinting :Construction, Erasure and Pirate Tracing” Journal of Universal Computer Science, vol. 11, no. 1 pp.122-149 (2005)
[43] R. Safavi-Naini and Y. Wang, “Collusion Secure q-ary Fingerprinting for perceptual content “Proceedings SPDRM 01, Springer Publishing, Heidelberg/NewYork, pp. 57-75 (2002).
[44] Chong Shangguan, Jingxue Ma and Gennian Ge “New Upper Upper Bounds for Parent-Identifying Codes and Traceability Codes” Des. Codes Cryptogr. DOI 10.1007/s10623-017-0420-y
[45] Simon R. Blackburn, “Frameproof Codes” SIAM Journal of Discrete Mathematics” vol. 16, no. 3, pp. 499-510.
[46] Simon R. Blackburn and Tuvi Etzion “Prolific Codes with the Identifiable Parent Property Codes”  SIAM Journal of Discrete Mathematics (2007).
[47] Sudhir Batra “A new class of 2-IPP Codes” Journal of Informatics and Mathematical Sciences, vol. 5 no. 2, pp.65-76 (2013).
[48] T. Van, Trung and S. Maritosyan, “On a class of Traceability Codes” Design, Codes and Cryptography, vol. 31, no. 2, pp.125-132 (2004).
[49] Xiande Zhang and Yeow Mang Chee, “Improved constructions of frameproof codes” https://doi.org/10.48550/arXiv.1206.5863
[50] Alok Tripathi, Rajiv Pandey and Amarjeet Singh “Boneh-Shaw fingerprint code and Tardos code analysis and optimization in minority collusion attack.” https://doi.org/10.1016/j.measen.2024.101173
[51] Zhandry, “New Techniques for Traitor Tracing: Size N(1/3) and More from Pairings (2020) “https://ia.cr/2020/954
[52] Zhandry, “WhiteBox Traitor Tracing” (2021) https://eprint.iacr.org/2021/891.
[53] Simon Blackburn,”An upper bound on the size of a code with the k-identifiable parent property”; https://ia.cr/2002/101
[54] Silverberg, Staddon and Walker,” Efficient Traitor Tracing Algorithms using List   Decoding”. https://ia.cr/2001/016  
[55] Anu Kathuria, “Traceable Codes Constructed from Certain Combinatorial Designs”,  Journal of Discrete Mathematics and Cryptography, vol. 27, issue 8,  pp.2473-2482 (2024).
[56] Anu Kathuria, “Optimizing Traceable Codes Through Latin Squares and Projective Planes” Journal of Discrete Mathematics and Cryptography, https ://doi/10.4974/JDMSC-2301

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