Strongly separable codes

详细信息    查看全文

• 作者：Jing Jiang ; Minquan Cheng ; Ying Miao
• 关键词：Multimedia fingerprinting ; Separable code ; Strongly separable code ; Frameproof code ; Tracing algorithm
• 刊名：Designs, Codes and Cryptography
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：79
• 期：2
• 页码：303-318
• 全文大小：492 KB
• 参考文献：1.Alon N., Cohen G., Krivelevich M., Litsyn S.: Generalized hashing and parent-identifying codes. J. Comb. Theory Ser. A 104, 207–215 (2003).
  2.Bazrafshan M., van Trung T.: On optimal bounds for separating hash families. Presented at the Germany Africa Workshop on Information and Communication Technology, Essen, Germany (2008).
  3.Blackburn S.R.: Frameproof codes. SIAM J. Discret. Math. 16, 499–510 (2003).
  4.Boneh D., Shaw J.: Collusion-secure fingerprinting for digital data. IEEE Trans. Inf. Theory 44, 1897–1905 (1998).
  5.Cheng M., Miao Y.: On anti-collusion codes and detection algorithms for multimedia fingerprinting. IEEE Trans. Inf. Theory 57, 4843–4851 (2011).
  6.Cheng M., Ji L., Miao Y.: Separable codes. IEEE Trans. Inf. Theory 58, 1791–1803 (2012).
  7.Cheng M., Fu H.-L., Jiang J., Lo Y.-H., Miao Y.: New bounds on \(\overline{2}\) -separable codes of length 2. Des. Codes Cryptogr. 74, 31–40 (2015).
  8.Cox I.J., Kilian J., Leighton F.T., Shamoon T.G.: Secure spread spectrum watermarking for multimedia. IEEE Trans. Image Process. 6, 1673–1687 (1997).
  9.Gao F., Ge G.: New bounds on separable codes for multimedia fingerprinting. IEEE Trans. Inf. Theory 60, 5257–5262 (2014).
  10.Liu K.J.R., Trappe W., Wang Z.J., Wu M., Zhao H.: Multimedia Fingerprinting Forensics for Traitor Tracing. Hindawi Publishing Corporation, New York (2005).
  11.MacWilliams F.J., Sloane N.J.A.: The Theory of Error-Correcting Codes. North-Holland, Amsterdam (1977).
  12.Podilchuk C.I., Zeng W.: Image-adaptive watermarking using visual models. IEEE J. Sel. Areas Commun. 16, 525–539 (1998).
  13.Stinson D.R., van Trung T., Wei R.: Secure frameproof codes, key distribution pattern, group testing algorithms and related structures. J. Stat. Plan. Infer. 86, 595–617 (2000).
  14.Trappe W., Wu M., Wang Z.J., Liu K.J.R.: Anti-collusion fingerprinting for multimedia. IEEE Trans. Sig. Process. 51, 1069–1087 (2003).
  
• 作者单位：Jing Jiang (1)
  Minquan Cheng (2)
  Ying Miao (3)
  
  1. Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki, 305-8573, Japan
  2. Guangxi Key Lab of Multi-source Information Mining & Security, Guangxi Normal University, Guilin, 541004, People’s Republic of China
  3. Faculty of Engineering, Information and Systems, University of Tsukuba, Tsukuba, Ibaraki, 305-8573, Japan
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Combinatorics
  Coding and Information Theory
  Data Structures, Cryptology and Information Theory
  Data Encryption
  Discrete Mathematics in Computer Science
  Information, Communication and Circuits
  
• 出版者：Springer Netherlands
• ISSN：1573-7586

文摘

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.