[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
Skip to main content

A Classification of Viruses Through Recursion Theorems

  • Conference paper
Computation and Logic in the Real World (CiE 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4497))

Included in the following conference series:

Abstract

We study computer virology from an abstract point of view. Viruses and worms are self-replicating programs, whose constructions are essentially based on Kleene’s second recursion theorem. We show that we can classify viruses as solutions of fixed point equations which are obtained from different versions of Kleene’s second recursion theorem. This lead us to consider four classes of viruses which various polymorphic features. We propose to use virus distribution in order to deal with mutations.

Topics covered. Computability theoretic aspects of programs, computer virology.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  • Adleman, L.: An abstract theory of computer viruses. In: Vulkov, L.G., Waśniewski, J., Yalamov, P. (eds.) NAA 2000. LNCS, vol. 403, Springer, Heidelberg (1988)

    Google Scholar 

  • Blum, M.: A machine-independent theory of the complexity of recursive functions. Journal of the Association for Computing Machinery 14(2), 322–336 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  • Bonfante, G., Kaczmarek, M., Marion, J.-Y.: Toward an abstract computer virology. In: Van Hung, D., Wirsing, M. (eds.) ICTAC 2005. LNCS, vol. 3722, pp. 579–593. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  • Bonfante, G., Kaczmarek, M., Marion, J.-Y.: On abstract computer virology from a recursion-theoretic perspective. Journal in Computer Virology, 1(3-4) (2006)

    Google Scholar 

  • Case, J.: Periodicity in generations of automata. Theory of Computing Systems 8(1), 15–32 (1974)

    MathSciNet  MATH  Google Scholar 

  • Chess, D., White, S.: An undetectable computer virus. In: Proceedings of the 2000 Virus Bulletin Conference (VB2000) (2000)

    Google Scholar 

  • Cohen, F.: Computer Viruses. PhD thesis, University of Southern California (January 1986)

    Google Scholar 

  • Cohen, F.: On the implications of computer viruses and methods of defense. Computers and Security 7, 167–184 (1988)

    Article  Google Scholar 

  • Filiol, E.: Computer Viruses: from Theory to Applications. Springer, Heidelberg (2005)

    MATH  Google Scholar 

  • Hansen, T., Nikolajsen, T., Träff, J., Jones, N.: Experiments with implementations of two theoretical constructions. In: Meyer, A.R., Taitslin, M.A. (eds.) Logic at Botik 1989. LNCS, vol. 363, pp. 119–133. Springer, Heidelberg (1989)

    Chapter  Google Scholar 

  • Jones, N.: Computer implementation and applications of kleene’s S-m-n and recursive theorems. In: Moschovakis, Y.N. (ed.) Lecture Notes in Mathematics, Logic From Computer Science, pp. 243–263. Springer, Heidelberg (1991)

    Google Scholar 

  • Jones, N.: Constant Time Factors Do Matter. MIT Press, Cambridge, MA, USA (1997)

    MATH  Google Scholar 

  • Kleene, S.: Introduction to Metamathematics. Van Nostrand (1952)

    Google Scholar 

  • Ludwig, M.: The Giant Black Book of Computer Viruses. American Eagle Publications (1998)

    Google Scholar 

  • Moss, L.: Recursion theorems and self-replication via text register machine programs. In: EATCS bulletin (2006)

    Google Scholar 

  • Rogers, H.: Theory of Recursive Functions and Effective Computability. McGraw Hill, New York (1967)

    MATH  Google Scholar 

  • Smullyan, R.: Recursion Theory for Metamathematics. Oxford University Press, Oxford (1993)

    MATH  Google Scholar 

  • Smullyan, R.: Diagonalization and Self-Reference. Oxford University Press, Oxford (1994)

    MATH  Google Scholar 

  • Thompson, K.: Reflections on trusting trust. Communications of the Association for Computing Machinery 27(8), 761–763 (1984)

    Article  Google Scholar 

  • von Neumann, J.: Theory of Self-Reproducing Automata (edited and completed by A.W.Burks). University of Illinois Press, Urbana, Illinois (1966)

    Google Scholar 

  • Zuo, Z., Zhou, M.: Some further theoretical results about computer viruses. The Computer Journal 47(6), 627–633 (2004)

    Article  Google Scholar 

  • Zuo, Z., Zhu, Q.-x., Zhou, M.-t.: On the time complexity of computer viruses. IEEE Transactions on information theory 51(8), 2962–2966 (2005)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bonfante, G., Kaczmarek, M., Marion, JY. (2007). A Classification of Viruses Through Recursion Theorems. In: Cooper, S.B., Löwe, B., Sorbi, A. (eds) Computation and Logic in the Real World. CiE 2007. Lecture Notes in Computer Science, vol 4497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73001-9_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-73001-9_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73000-2

  • Online ISBN: 978-3-540-73001-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics