TY - JOUR
T1 - Bounds on Traceability Schemes
AU - Gu, Yujie
AU - Miao, Ying
N1 - Funding Information:
Manuscript received December 7, 2016; revised August 14, 2017; accepted October 11, 2017. Date of publication October 26, 2017; date of current version April 19, 2018. Y. Miao was supported by JSPS Grant-in-Aid for Scientific Research (C) under Grant 15K04974. Y. Gu is with the Department of Policy and Planning Sciences, Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba 305-8573, Japan (e-mail: s1530147@u.tsukuba.ac.jp). Y. Miao is with the Faculty of Engineering, Information and Systems, University of Tsukuba, Tsukuba 305-8573, Japan (e-mail: miao@sk.tsukuba.ac.jp). Communicated by F. Oggier, Associate Editor for Coding Theory. Digital Object Identifier 10.1109/TIT.2017.2766659
PY - 2018/5
Y1 - 2018/5
N2 - The Stinson-Wei traceability scheme (known as traceability scheme) was proposed for broadcast encryption as a generalization of the Chor-Fiat-Naor traceability scheme (known as traceability code). Cover-free family was introduced by Kautz and Singleton in the context of binary superimposed code. In this paper, we find a new relationship between a traceability scheme and a cover-free family, which strengthens the anti-collusion strength from t to t2, i.e., a t-traceability scheme is a t2-cover-free family. Based on this interesting discovery, we derive new upper bounds for traceability schemes. By using combinatorial structures, we construct several infinite families of optimal traceability schemes, which attain our new upper bounds. We also provide a constructive lower bound for traceability schemes, the size of which has the same order of magnitude as our general upper bound. Meanwhile, we consider parent-identifying set systems, an anti-collusion key-distributing scheme requiring weaker conditions than traceability scheme but stronger conditions than cover-free family. A new upper bound is also given for parent-identifying set systems.
AB - The Stinson-Wei traceability scheme (known as traceability scheme) was proposed for broadcast encryption as a generalization of the Chor-Fiat-Naor traceability scheme (known as traceability code). Cover-free family was introduced by Kautz and Singleton in the context of binary superimposed code. In this paper, we find a new relationship between a traceability scheme and a cover-free family, which strengthens the anti-collusion strength from t to t2, i.e., a t-traceability scheme is a t2-cover-free family. Based on this interesting discovery, we derive new upper bounds for traceability schemes. By using combinatorial structures, we construct several infinite families of optimal traceability schemes, which attain our new upper bounds. We also provide a constructive lower bound for traceability schemes, the size of which has the same order of magnitude as our general upper bound. Meanwhile, we consider parent-identifying set systems, an anti-collusion key-distributing scheme requiring weaker conditions than traceability scheme but stronger conditions than cover-free family. A new upper bound is also given for parent-identifying set systems.
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U2 - 10.1109/TIT.2017.2766659
DO - 10.1109/TIT.2017.2766659
M3 - Article
AN - SCOPUS:85032434435
VL - 64
SP - 3450
EP - 3460
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
SN - 0018-9448
IS - 5
ER -