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Theoretical Foundation for Code Obfuscation Security: A Kolmogorov Complexity Approach

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E-Business and Telecommunications (ICETE 2015)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 585))

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Abstract

The main problem in designing effective code obfuscation is to guarantee security. State of the art obfuscation techniques rely on an unproven concept of security, and therefore are not regarded as provably secure. In this paper, we undertake a theoretical investigation of code obfuscation security and its adversary model based on Kolmogorov complexity and algorithmic mutual information. We introduce a new definition of code obfuscation that requires the algorithmic mutual information between a code and its obfuscated version to be minimal, allowing for controlled amount of information to be leaked to an adversary. We argue that our definition avoids the impossibility results of Barak et al. and is more advantageous than the obfuscation indistinguishability definition in the sense it is more intuitive, and is algorithmic rather than probabilistic.

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Notes

  1. 1.

    The security parameter may include the obfuscation key, the obfuscation transformation algorithm or any necessary information that the obfuscation function can use.

  2. 2.

    An opaque predicate is an algebraic expression which always evaluates to same value (true or false) regardless of the input.

  3. 3.

    It is possible to parameterize the amount of information, but we think it would add much complication for little gain.

  4. 4.

    If this can not be checked, e.g. due to a large function domain, the adversary must provide a formal proof that the functionality is the same.

  5. 5.

    Or rather, a circuit or a Turing machine representation thereof.

  6. 6.

    That is, we run \( R \) to produce \( P' \) then we execute the result of this first execution, that is \( P \) itself.

  7. 7.

    The \( O(1) \) term is absorbed by the logarithmic additive term that we are not notating.

  8. 8.

    Which is proved to be an unconditionally secure symmetric cypher.

References

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Author information

Authors and Affiliations

  1. Department of Computing, Imperial College London, London, UK

    Rabih Mohsen

  2. Information Security Group, Royal Holloway University of London, London, UK

    Alexandre Miranda Pinto

  3. Instituto Universitário da Maia, Maia, Portugal

    Alexandre Miranda Pinto

Authors
  1. Rabih Mohsen
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  2. Alexandre Miranda Pinto
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Corresponding author

Correspondence to Rabih Mohsen .

Editor information

Editors and Affiliations

  1. Dept. of Computer & Info Science, Fordham University, Bronx, New York, USA

    Mohammad S. Obaidat

  2. IUT, University of Haute Alsace, Colmar, France

    Pascal Lorenz

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Mohsen, R., Pinto, A.M. (2016). Theoretical Foundation for Code Obfuscation Security: A Kolmogorov Complexity Approach. In: Obaidat, M., Lorenz, P. (eds) E-Business and Telecommunications. ICETE 2015. Communications in Computer and Information Science, vol 585. Springer, Cham. https://doi.org/10.1007/978-3-319-30222-5_12

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  • DOI: https://doi.org/10.1007/978-3-319-30222-5_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30221-8

  • Online ISBN: 978-3-319-30222-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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