Skip to main content

Improved Results on Algebraic Cryptanalysis of A5/2

  • Conference paper

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 12))

Abstract

Algebraic analysis of A5/2, the weaker version of GSM encryption algorithm, is presented in this article. We have enhanced existing cryptanalysis of A5/2 in terms of data requirement. Experimental results using an implementation of Groebner basis algorithm are presented. It has been found that state bits of the cipher can be recovered in fewer number of data frames than required in a previous efficient attack against GSM communication. Number of data frames required for both known-plaintext and ciphertext-only attacks can be reduced if linearization is replaced by Groebner basis technique without changing the time complexity of attack.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bogodanov, A., Eisenbarth, T., Rupp, A.: A Hardware-Assisted Realtime Attack on A5/2 Without Precomputations. In: Paillier, P., Verbauwhede, I. (eds.) CHES 2007. LNCS, vol. 4727, pp. 394–412. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  2. Kipnis, A., Shamir, A.: Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization. In: Wiener, M.J. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 19–30. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  3. Buchberger, B.: Groebner Bases: An Algorithmic Method in Polynomial Ideal Theory. Multidimensional System Theory, 184–232 (1985)

    Google Scholar 

  4. Yin Yang, B., Ming Chen, J.: Theoretical Analysis of XL over Small Fields. In: Wang, H., Pieprzyk, J., Varadharajan, V. (eds.) ACISP 2004. LNCS, vol. 3108, pp. 277–288. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  5. Barkan, E., Biham, E., Keller, N.: Instant Ciphertext-Only Cryptanalysis of GSM Encrypted Communication. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 600–616. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  6. Biham, E., Dunkelman, O.: Cryptanalysis of the A5/1 GSM Stream Cipher. In: Roy, B., Okamoto, E. (eds.) INDOCRYPT 2000. LNCS, vol. 1977, pp. 43–51. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  7. Armknecht, F., Karuse, M.: Algebraic Attacks on Combiners with Memory. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 162–176. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  8. Armknecht, F.: Improving Fast Algebraic Attacks. In: Roy, B., Meier, W. (eds.) FSE 2004. LNCS, vol. 3017, pp. 65–82. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  9. Goldberg, I., Wagner, D., Green, L.: The Real-Time Cryptanalysis of A5/2. In: Rump Session of Crypto 1999 (1999)

    Google Scholar 

  10. Faugere, J.C.: A New Efficient Algorithm for Computing Groebner Bases (F4). Journal of Pure and Applied Algebra 139(1-3), 61–88 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  11. Faugere, J.C.: A New Efficient Algorithm for Computing Groebner Bases without Reduction to Zero (F5). In: International Symposium on Symbolic and Algebraic Computation ISSAC 2002, pp. 75–83. ACM Press, New York (2002)

    Chapter  Google Scholar 

  12. Faugere, J.C., Joux, A.: Algebraic Cryptanalysis of Hidden Field Equation (HFE) Cryptosystem Using Groebner Bases. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 44–60. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  13. Golic, J.D.: Cryptanalysis of Alleged A5 Stream Cipher. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 239–255. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  14. Golic, J.D., O’ Conner, L.: Embedding and Probabilistic Correlation Attacks on Clock-Controlled Shift Registers. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 90–100. Springer, Heidelberg (1995)

    Google Scholar 

  15. MAGMA Computational Algebra System, http://magma.maths.usyd.edu.au/

  16. Afzal, M., Masood, A.: On Generating Algebraic Equations for A5-Type Key Stream Generator. In: Trends in Intelligent Systems and Computer Engineering Series. LNEE, vol. 6, pp. 443–451. Springer, US; An extended vesrion of Algebraic Attack on A5-Type Irregularly Clocked Key Stream Generator. In: Proc. International Multiconference of Engineers and Computer Scientists-IMECS 2007, IAENG (March 2007)

    Google Scholar 

  17. Briceno, M., Goldberg, I., Wagner, D.: A Pedagogical Implementation of the GSM A5/1 and A5/2 Voice Privacy Encryption Algorithms (1999), http://cryptome.org/gsm-a512.htm (Originally on www.scard.org)

  18. Krause, M.: BDD-Based Cryptanalysis of Keystream Generators. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 222–237. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  19. Sugita, M., Kawazoe, M., Imai, H.: Relation between XL Algorithm and Groebner Bases Algorithm, IACR e-print Server, http://eprint.iacr.org//2004/112/

  20. Courtois, N.: Algebraic Attacks on Combiners with Memory and Several Outputs. In: Park, C.-s., Chee, S. (eds.) ICISC 2004. LNCS, vol. 3506, pp. 3–20. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  21. Courtois, N.: Fast Algebraic Attacks on Stream Ciphers with Linear Feedback. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 176–194. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  22. Courtois, N., Pieprzyk, J.: Cryptanalysis of Block Ciphers with Over-defined Systems of Equations. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 267–287. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  23. Courtois, N.: Higher Order Correlation Attacks, XL algorithm and Cryptanalysis of Toyocrypt. In: Lee, P.J., Lim, C.H. (eds.) ICISC 2002. LNCS, vol. 2587, pp. 182–199. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  24. Courtois, N.: The Security of Hidden Field Equations (HFE). In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol. 2020, pp. 266–281. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  25. Courtois, N., Meier, W.: Algebraic Attacks on Stream Ciphers with Linear Feedback. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 346–359. Springer, Heidelberg (2003)

    Google Scholar 

  26. Courtois, N., Pieprzyk, J.: Cryptanalysis of Block Ciphers with Overdefined Systems of Equations. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 267–287. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  27. Ekdahl, P., Johansson, T.: Another Attack on A5/1. IEEE Transactions on Information Theory 49(1), 284–288 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  28. Al-Hinai, S., Batten, L., Colbert, B.: Mutually Clock-Controlled Feedback Shift Registers Provide Resistance to Algebraic Attacks. In: Conference Proceedings: 8th International Conference on Finite Fields and Applications (FQ8) (July 2007)

    Google Scholar 

  29. Petrovic, S., Fuster-Sabater, A.: Cryptanalysis of the A5/2 Algorithm, IACR ePrint Report 200/52 (2000), http://eprint.iacr.org

  30. Biryukov, T.A., Shamir, A., Wagner, D.: Real Time Cryptanalysis of A5/1 on a PC. In: Schneier, B. (ed.) FSE 2000. LNCS, vol. 1978, pp. 1–18. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  31. Johansson, T., Jonsson, F.: Improved Fast Correlation Attack on Stream Ciphers via Convolutional Codes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 347–362. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  32. Pornin, T., Stern, J.: Software-Hardware Trade-Offs: Application to A5/1 Cryptanalysis. In: Paar, C., Koç, Ç.K. (eds.) CHES 2000. LNCS, vol. 1965, pp. 318–327. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  33. Meier, W., Staffelbach, O.: Fast Correlation Attacks on Certain Stream Ciphers. Journal of Cryptology 1(3), 159–176 (1989)

    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

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Afzal, M., Masood, A., Shehzad, N. (2008). Improved Results on Algebraic Cryptanalysis of A5/2. In: Jahankhani, H., Revett, K., Palmer-Brown, D. (eds) Global E-Security. ICGeS 2008. Communications in Computer and Information Science, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69403-8_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-69403-8_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69402-1

  • Online ISBN: 978-3-540-69403-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics