On non-binary traceability set systems

We introduce non-binary IPP set systems with traceability properties that have IPP codes and binary IPP set systems with traceability capabilities as particular cases. We prove an analogue of the Gilbert–Varshamov bound for such systems.

[1]  E. E. Egorova Generalization of IPP Codes and IPP Set Systems , 2019, Probl. Inf. Transm..

[2]  Jean-Paul M. G. Linnartz,et al.  On Codes with the Identifiable Parent Property , 1998, J. Comb. Theory, Ser. A.

[3]  Gérard D. Cohen,et al.  A Hypergraph Approach to the Identifying Parent Property: The Case of Multiple Parents , 2001, SIAM J. Discret. Math..

[4]  Tina Lindkvist,et al.  A class of traceability codes , 2002, IEEE Trans. Inf. Theory.

[5]  Gregory A. Kabatiansky On the Tracing Traitors Math - Dedicated to the Memory of Bob Blakley - Pioneer of Digital Fingerprinting and Inventor of Secret Sharing , 2019, C2SI.

[6]  G. A. Kabatiansky,et al.  Traceability Codes and Their Generalizations , 2019, Probl. Inf. Transm..

[7]  Gregory A. Kabatiansky,et al.  Analysis of Two Tracing Traitor Schemes via Coding Theory , 2017, ICMCTA.

[8]  Ying Miao,et al.  Bounds on Traceability Schemes , 2016, IEEE Transactions on Information Theory.

[9]  Amos Fiat,et al.  Tracing traitors , 2000, IEEE Trans. Inf. Theory.

[10]  Douglas R. Stinson,et al.  Combinatorial Properties and Constructions of Traceability Schemes and Frameproof Codes , 1998, SIAM J. Discret. Math..

[11]  Simon R. Blackburn Surveys in Combinatorics 2003: Combinatorial schemes for protecting digital content , 2003 .

[12]  Michael J. Collins Upper bounds for parent-identifying set systems , 2009, Des. Codes Cryptogr..

[13]  Douglas R. Stinson,et al.  Key Preassigned Traceability Schemes for Broadcast Encryption , 1998, Selected Areas in Cryptography.

[14]  E. Egorova,et al.  New lower bound on the rate of traceability set systems , 2019, 2019 XVI International Symposium "Problems of Redundancy in Information and Control Systems" (REDUNDANCY).

[15]  G. R. BLAKLEY Safeguarding cryptographic keys , 1979, 1979 International Workshop on Managing Requirements Knowledge (MARK).

[16]  Tuvi Etzion,et al.  Traceability codes , 2009, J. Comb. Theory, Ser. A.

[17]  Minquan Cheng,et al.  Probabilistic Existence Results for Parent-Identifying Schemes , 2019, IEEE Transactions on Information Theory.

[18]  Gérard D. Cohen,et al.  Generalized hashing and parent-identifying codes , 2003, J. Comb. Theory, Ser. A.

[19]  Reihaneh Safavi-Naini,et al.  New results on frame-proof codes and traceability schemes , 2001, IEEE Trans. Inf. Theory.

[20]  Marcel Fernandez,et al.  A Construction of Traceability Set Systems with Polynomial Tracing Algorithm , 2019, 2019 IEEE International Symposium on Information Theory (ISIT).

[21]  Jessica Staddon,et al.  Combinatorial properties of frameproof and traceability codes , 2001, IEEE Trans. Inf. Theory.

[22]  Adi Shamir,et al.  How to share a secret , 1979, CACM.

[23]  Dalit Naor,et al.  Broadcast Encryption , 1993, Encyclopedia of Multimedia.

[24]  Jan-Åke Larsson,et al.  Comments on "New Results on Frame-Proof Codes and Traceability Schemes" , 2010, IEEE Trans. Inf. Theory.

[25]  P. Erdös,et al.  Families of finite sets in which no set is covered by the union ofr others , 1985 .