Designs, Codes and Cryptography

, Volume 80, Issue 1, pp 11–28 | Cite as

Almost separating and almost secure frameproof codes over \(q\)-ary alphabets

  • José Moreira
  • Marcel Fernández
  • Grigory Kabatiansky


In this paper we discuss some variations of the notion of separating code for alphabets of arbitrary size. We show how the original definition can be relaxed in two different ways, namely almost separating and almost secure frameproof codes, yielding two different concepts. The new definitions enable us to obtain codes of higher rate, at the expense of satisfying the separating property partially. These new definitions become useful when complete separation is only required with high probability, rather than unconditionally. We also show how the codes proposed can be used to improve the rate of existing constructions of families of fingerprinting codes.


Separating code Secure frameproof code Fingerprinting Traitor tracing 

Mathematics Subject Classification

94B60 94B65 



We would like to thank the anonymous Reviewers, whose insightful comments and observations helped to improve the contents and presentation of the paper. J. Moreira and M. Fernández have been supported in part by the Spanish Government through Projects Consolider-Ingenio 2010 CSD2007-00004 “ARES” and TEC2011-26491 “COPPI”, and by the Catalan Government through Grant 2014 SGR-1504. G. Kabatiansky has been supported in part by the Russian Foundation for Basic Research through Grants RFBR 13-01-12458, RFBR 13-07-00978, and RFBR 14-01-93108.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • José Moreira
    • 1
    • 2
  • Marcel Fernández
    • 1
  • Grigory Kabatiansky
    • 3
    • 4
  1. 1.Department of Network EngineeringUniversitat Politècnica de Catalunya (UPC)BarcelonaSpain
  2. 2.SCYTL Secure Electronic VotingBarcelonaSpain
  3. 3.National Research University Higher School of Economics (HSE)MoscowRussia
  4. 4.Institute for Information Transmission ProblemsRussian Academy of SciencesMoscowRussia

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