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Full Characterization of a Class of Graphs Tailored for Software Watermarking

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Abstract

Digital watermarks have been regarded as a promising way to fight copyright violations in the software industry. In some graph-based watermarking schemes, identification data is disguised as control-flow graphs of dummy code. Recently, Chroni and Nikolopoulos proposed an ingenious such scheme whereby an integer is encoded into a particular kind of permutation graph. We give a formal characterization of the class of graphs generated by their encoding function, which we call canonical reducible permutation graphs. A linear-time recognition algorithm is also given, setting the basis for a polynomial-time algorithm to restore watermarks that underwent the malicious removal of some edges. Finally, we give a simpler decoding algorithm for Chroni and Nikolopoulos’ watermarks.

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References

  1. Allen, F.E.: Control flow analysis. SIGPLAN Not. 5, 1–19 (1970)

    Article  Google Scholar 

  2. Bento, L.M.S., Boccardo, D., Machado, R.C.S., Pereira de Sá, V.G., Szwarcfiter, J.L.: On the resilience of canonical reducible permutation graphs. Discrete Appl. Math. 234, 32–46 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  3. Business Software Alliance.: Shadow Market: 2011 BSA Global Software Piracy Study. http://globalstudy.bsa.org (2012)

  4. Chroni, M., Nikolopoulos, S.D.: Efficient encoding of watermark numbers as reducible permutation graphs, arXiv:1110.1194v1 [cs.DS] (2011)

  5. Chroni, M., Nikolopoulos, S.D.: Encoding watermark numbers as cographs using self-inverting permutations. In: Proceeding of 12th International Conference on Computer Systems and Technologies, CompSysTech’11, ACM ICPS, vol. 578, pp. 142–148 (2011) (Best Paper Award)

  6. Chroni, M., Nikolopoulos, S.D.: An efficient graph codec system for software watermarking. In: IEEE Proceedings of 36th IEEE Conference on Computers, Software and Applications, COMPSAC’12, pp. 595–600 (2012)

  7. Chroni, M., Nikolopoulos, S.D.: Multiple encoding of a watermark number into reducible permutation graphs using cotrees. In: ACM ICPS Proceedings of 13th International Conference on Computer Systems and Technologies, CompSysTech’12, pp. 118–125 (2012)

  8. Chroni, M., Nikolopoulos, S.D.: An embedding graph-based model for software watermarking. In: IEEE Proceedings 8th International Conference on Intelligent Information Hiding and Multimedia Signal Processing, IIH-MSP’12, pp. 261–264 (2012)

  9. Collberg, C., Thomborson, C.: Software watermarking: models and dynamic embeddings. In: Proceedings 26th ACM SIGPLAN-SIGACT on Principles of Programming Languages, POPL’99, pp. 311–324 (1999)

  10. Collberg, C., Kobourov, S., Carter, E., Thomborson, C.: Error-correcting graphs for software watermarking. In: Proceedings 29th Workshop on Graph-Theoretic Concepts in Computer Science, WG’03, vol. 2880, pp. 156–167. LNCS (2003)

  11. Collberg, C., Thomborson, C., Townsend, G.: Dynamic graph-based software fingerprinting. ACM Trans. Program. Lang. Syst. 29, 1–67 (2007)

    Article  Google Scholar 

  12. Collberg, C., Huntwork, A., Carter, E., Townsend, G., Stepp, M.: More on graph theoretic software watermarks: implementation, analysis and attacks. Inf. Softw. Technol. 51, 56–67 (2009)

    Article  Google Scholar 

  13. Collberg, C.: SandMark: A Tool for the Study of Software Protection Algorithms. http://sandmark.cs.arizona.edu/index.html (2013) Accessed 25 Nov 2013

  14. Davidson, R.L., Myhrvold, N.: Method and system for generating and auditing a signature for a computer program, US Patent 5.559.884, Microsoft Corporation (1996)

  15. Hamilton, J., Danicic, S.: A survey of static software watermarking. In: Proceedings World Congress on Internet Security, WorldCIS’11, pp. 100–107 (2011)

  16. Hecht, M.S., Ullman, J.D.: Flow graph reducibility. SIAM J. Comput. 1, 188–202 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  17. Hecht, M.S., Ullman, J.D.: Characterizations of reducible flow graphs. J. ACM 21, 367–375 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  18. Nielson, F., Nielson, H.R., Hankin, C.: Principles of Program Analysis. Springer, Berlin (2004)

    MATH  Google Scholar 

  19. Raghavan, V., Spinrad, J.: Robust Algorithms for Restricted Domains. In: Proceedings of 12th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA’01, pp. 460–467 (2001)

  20. Schaefer, I., Rabiser, R., Clarke, D., Bettini, L., Benavides, D., Botterweck, G., Pathak, A., Trujillo, S., Villela, K.: Software diversity: state of the art and perspectives. Int. J. Softw. Tools Technol. Transf. 14, 477–495 (2012)

    Article  Google Scholar 

  21. Su, Y., Liu, J., Li, D.: Hiding Signatures in Variable Names. Communications in Computer and Information Science, pp. 333–340. Springer, Berlin (2013)

    Google Scholar 

  22. Tarjan, R.E.: Testing flow graph reducibiliy. J. Comput. Syst. Sci. 9, 355–365 (1974)

    Article  MATH  Google Scholar 

  23. Venkatesan, R., Vazirani, V., Sinha, S.: A graph theoretic approach to software watermarking. In: Proceedings 4th International Information Hiding Workshop, pp. 157–168 (2001)

  24. Venkatesan, R., Vazirani, V.: Technique for producing through watermarking highly tamper-resistant executable code and resulting watermarked code so formed, Microsoft Corporation, US Patent: 7051208 (2006)

  25. Wichmann, B.A., Canning, A.A., Clutterbuck, D.L., Winsborrow, L.A., Ward, N.J., Marsh, D.W.R.: Industrial perspective on static analysis. Softw. Eng. J. 10, 69–75 (1995)

    Article  Google Scholar 

  26. Zhu, J., Liu, Y., Yin, K.: A novel dynamic graph software watermark scheme. In: Proceedings of 1st International Workshop on Education Technology and Computer Science, vol. 3, pp. 775–780 (2009)

  27. Zhu, W., Thomborson, C., Wang, F-Y.: A survey of software watermarking. In: Proceedings IEEE International Conference on Intelligence and Security Informatics, ISI’05, pp. 454–458 (2005)

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Acknowledgements

Funding was provided by Conselho Nacional de Desenvolvimento Cientìfico e Tecnológico (Grant Nos. 400609/2015-0, 487061/2013-6, 309234/2015-8, 421007/2016-8), Pronametro (Grant No. 52600.017257/2013), Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro (BR) (Grant Nos. JCNE-203889, TECNOVA-143360) and Financiadora de Estudos e Projetos (Grant No. TI-MAIOR-SBV936).

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Authors and Affiliations

  1. Univ. Federal do Rio de Janeiro, Rio de Janeiro, Brazil

    Lucila M. S. Bento, Vinícius G. Pereira de Sá & Jayme L. Szwarcfiter

  2. Inst. Nac. de Metrologia, Qualidade e Tecnologia, Rio de Janeiro, Brazil

    Davidson R. Boccardo & Raphael C. S. Machado

Authors
  1. Lucila M. S. Bento
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  2. Davidson R. Boccardo
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  3. Raphael C. S. Machado
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  4. Vinícius G. Pereira de Sá
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  5. Jayme L. Szwarcfiter
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Correspondence to Vinícius G. Pereira de Sá.

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Part of this paper was presented as an extended abstract entitled “Towards a provably resilient scheme for graph-based watermarking” at the 39th International Workshop on Graph Theoretic Concepts in Computer Science, WG 2013, and appeared in Lecture Notes in Computer Science8165 (2013), 50–63.

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Bento, L.M.S., Boccardo, D.R., Machado, R.C.S. et al. Full Characterization of a Class of Graphs Tailored for Software Watermarking. Algorithmica 81, 2899–2916 (2019). https://doi.org/10.1007/s00453-019-00557-w

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  • DOI: https://doi.org/10.1007/s00453-019-00557-w

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