Designs, Codes and Cryptography

, Volume 77, Issue 2–3, pp 301–319 | Cite as

On tight bounds for binary frameproof codes

  • Chuan Guo
  • Douglas R. Stinson
  • Tran van Trung


In this paper, we study \(w\)-frameproof codes, which are equivalent to \(\{1,w\}\)-separating hash families. Our main results concern binary codes, which are defined over an alphabet of two symbols. For all \(w \ge 3\), and for \(w+1 \le N \le 3w\), we show that an \({\mathsf {SHF}}(N; n,2, \{1,w \})\) exists only if \(n \le N\), and an \({\mathsf {SHF}}(N; N,2, \{1,w \})\) must be a permutation matrix of degree \(N\).


Code Frameproof code Hash family Separating hash family 

Mathematics Subject Classification




D. Stinson’s research is supported by NSERC discovery Grant 203114-11.


  1. 1.
    Bazrafshan, M., van Trung, T.: Bounds for separating hash families. J. Combin. Theory A 118, 1129–1135 (2011)zbMATHCrossRefGoogle Scholar
  2. 2.
    Blackburn, S.R.: Frameproof codes. SIAM J. Discrete Math. 16, 499–510 (2003)zbMATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Boneh, D., Shaw, J.: Collusion-free fingerprinting for digital data. IEEE Trans. Inform. Theory 44, 1897–1905 (1998)zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Chor, B., Fiat, A., Naor, M.: Tracing traitors. In: Desmedt, Y.G. (ed.) Advances in Cryptology—CRYPTO’94. Lecture Notes in Computer Science, vol. 839, pp. 257–270. Springer, Berlin (1994)Google Scholar
  5. 5.
    Colbourn C.J., Horsley D., Syrotiuk V.R.: Frameproof codes and compressive sensing, forty-eighth annual allerton conference, Allerton House, UIUC, Illinois, USA, Sept 29–Oct 1, 2010, 985–990 (2010)Google Scholar
  6. 6.
    Fiat, A., Tassa, T.: Dynamic traitor tracing. In: Weiner, M. (ed.) Advances in Cryptology—CRYPTO99. Lecture Notes in Computer Science, vol. 1666, pp. 354–371. Springer, Berlin (1999)Google Scholar
  7. 7.
    Sarkar P., Stinson D.R.: Frameproof and IPP Codes, Progress in Cryptology—Indocrypt. Lecture Notes in Computer Science. Springer, Berlin (2001)Google Scholar
  8. 8.
    Shangguan C., Wang X., Ge G. and Miao Y.: New Bounds For Frameproof Codes. Preprint, 2014.
  9. 9.
    Staddon, J.N., Stinson, D.R., Wei, R.: Combinatorial properties of frameproof and traceability codes. IEEE Trans. Inform. Theory 47, 1042–1049 (2001)zbMATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Stinson, D.R., van Trung, T., Wei, R.: Secure frameproof codes, key distribution patterns, group testing algorithms and related structures. J. Statist. Plan. Inference 86, 595–617 (2000)zbMATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Stinson, D.R., Wei, R.: Combinatorial properties and constructions of traceability schemes and frameproof codes. SIAM J. Discrete Math. 11, 41–53 (1998)zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    van Trung, Tran: A tight bound for frameproof codes viewed in terms of separating hash families. Des. Codes Cryptogr. 72, 713–718 (2014)zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Chuan Guo
    • 1
  • Douglas R. Stinson
    • 1
  • Tran van Trung
    • 2
  1. 1.David R. Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada
  2. 2.Institut für Experimentelle MathematikUniversität Duisburg-EssenEssenGermany

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