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Strongly separable codes

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Abstract

Binary \(t\)-frameproof codes (\(t\)-FPCs) are used in multimedia fingerprinting schemes where the identification of authorized users taking part in the averaging collusion attack is required. In this paper, a binary strongly \(\overline{t}\)-separable code (\(\overline{t}\)-SSC) is introduced to improve such a scheme based on a binary \(t\)-FPC. A binary \(\overline{t}\)-SSC has the same traceability as a binary \(t\)-FPC but has more codewords than a binary \(t\)-FPC. A composition construction for binary \(\overline{t}\)-SSCs from \(q\)-ary \(\overline{t}\)-SSCs is described, which stimulates the research on \(q\)-ary \(\overline{t}\)-SSCs with short length. Several infinite series of optimal \(q\)-ary \(\overline{2}\)-SSCs of length \(2\) are derived from the fact that a \(q\)-ary \(\overline{2}\)-SSC of length \(2\) is equivalent to a \(q\)-ary \(\overline{2}\)-separable code of length \(2\). Combinatorial properties of \(q\)-ary \(\overline{2}\)-SSCs of length \(3\) are investigated, and a construction for \(q\)-ary \(\overline{2}\)-SSCs of length \(3\) is provided. These \(\overline{2}\)-SSCs of length \(3\) have more than \(12.5\,\%\) codewords than \(2\)-FPCs of length \(3\) could have.

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Acknowledgments

The authors express their sincere thanks to the two anonymous reviewers for their valuable comments and suggestions in revising this paper, and to the editor for his/her excellent editorial job. Cheng is supported in part by NSFC (No. 11301098), Guangxi Natural Science Foundations (No. 2013 GXNSFCA019001), and 2014GXNSFDA118001 and Program on the High Level Innovation Team and Outstanding Scholars in Universities of Guangxi Province. Miao is supported by JSPS Grant-in-Aid for Scientific Research (C) under Grant No. 24540111.

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Authors and Affiliations

  1. Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki, 305-8573, Japan

    Jing Jiang

  2. Guangxi Key Lab of Multi-source Information Mining & Security, Guangxi Normal University, Guilin, 541004, People’s Republic of China

    Minquan Cheng

  3. Faculty of Engineering, Information and Systems, University of Tsukuba, Tsukuba, Ibaraki, 305-8573, Japan

    Ying Miao

Authors
  1. Jing Jiang
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  2. Minquan Cheng
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  3. Ying Miao
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Correspondence to Jing Jiang.

Additional information

Communicated by L. Perret.

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Jiang, J., Cheng, M. & Miao, Y. Strongly separable codes. Des. Codes Cryptogr. 79, 303–318 (2016). https://doi.org/10.1007/s10623-015-0050-1

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  • DOI: https://doi.org/10.1007/s10623-015-0050-1

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