Skip to main content
SpringerLink
Log in

State cycles, initialization and the Trivium stream cipher

  • Published:
Cryptography and Communications Aims and scope Submit manuscript

Abstract

Trivium is a keystream generator for a binary additive synchronous stream cipher. It was selected in the final portfolio for the Profile 2 category of the eSTREAM project. The keystream generator is constructed using bit-based shift registers. In this paper we present an alternate representation of Trivium using word-based shift registers, with a word size of three bits. This representation is useful for determining cycles of internal state values. Under this representation it is clear that the state space can be partitioned into subspaces and that over some of these subspaces the state update function is effectively linear. The role of the initialization process is critical in ensuring the states used for generating keystream are updated nonlinearly at some point, as the state update function alone does not provide this.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Bernstein, D.: A reformulation of TRIVIUM. Submission to Phorum: ECRYPT forum, 20 February 2006. Available at http://www.ecrypt.eu.org/stream/phorum/read.php?1,448

  2. Courtois, N.: Fast algebraic attacks on stream ciphers with linear feedback. In: Boneh, D. (eds.) Advances in Cryptology—CRYPTO’03. Lecture Notes in Computer Science, vol. 2729, pp. 177–194. Springer, Berlin (2003)

    Google Scholar 

  3. de Canniere, C., Preneel, B.: Trivium specification. Submission to eSTREAM, ECRYPT Stream Cipher Project. Report 2005/030 (2005). Available at http://www.ecrypt.eu.org/stream/ciphers/trivium/trivium.pdf

  4. Dinur, I., Shamir, A.: Cube attacks on tweakable black box polynomials. In: Joux, A. (ed.) Advances in Cryptology—EUROCRYPT 2009. Lecture Notes in Computer Science, vol. 5479, pp. 278–299. Springer, Berlin (2009)

    Chapter  Google Scholar 

  5. Englund, H., Johansson, T., Turan, M.: A framework for chosen IV statistical analysis of stream ciphers. In: Srinathan, K., Pandu Rangan, C., Yung, M. (eds.) Progress in Cryptology—INDOCRYPT 2007. Lecture Notes in Computer Science, vol. 4859, pp. 268–281. Springer, Berlin (2007)

    Chapter  Google Scholar 

  6. eSTREAM: The ECRYPT Stream Cipher Project. Available at http://www.ecrypt.eu.org/stream/

  7. Hong, J.: Some trivial states of Trivium. Posted to eSTREAM Phorum, 7 September 2005

  8. Hong, J.: Certain pairs of key–IV pairs for Trivium. Posted to eSTREAM Phorum, 13 September 2005

  9. Hu, H., Gong, G.: Periods on two kinds of nonlinear feedback shift registers with time varying feedback functions. Int. J. Found. Comput. Sci. 22(6), 1317–1329 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. Khazaei, S.: Re: A reformulation of TRIVIUM. Submission to Phorum: ECRYPT forum, 21 February 2006. Available at http://www.ecrypt.eu.org/stream/phorum/read.php?1,448

  11. Khazaei, S., Hasanzadeh, M.: Linear sequential circuit approximation of the trivium stream cipher. eSTREAM, ECRYPT Stream Cipher Project, Report 2005/063 (2005). Available at http://www.ecrypt.eu.org/stream/papersdir/2005/063.pdf

  12. Maximov, A., Biryukov, A.: Two trivial attacks on trivium. eSTREAM, ECRYPT Stream Cipher Project, Report 2007/003 (2007). Available at http://www.ecrypt.eu.org/stream/papersdir/2007/003.pdf

  13. Raddum, H.: Cryptanalytic results on trivium. eSTREAM, ECRYPT Stream Cipher Project, Report 2006/039 (2006). Available at http://www.ecrypt.eu.org/stream/papersdir/2006/039.pdf

  14. Turan, M., Kara, O.: Linear approximations for 2-round trivium. eSTREAM, ECRYPT Stream Cipher Project, Report 2007/008 (2007). Available at http://www.ecrypt.eu.org/stream/papersdir/2007/008.pdf

  15. Vielhaber, M.: Breaking ONE.FIVIUM by AIDA an algebraic IV differential attack. IACR Cryptology eprint Archive, Report 2007/413 (2007). Available at http://eprint.iacr.org/2007/413.pdf

  16. Vielhaber, M.: AIDA breaks BIVIUM (A & B) in 1 minute dual core CPU time. IACR Cryptology eprint Archive, Report 2009/402 (2009). Available at http://eprint.iacr.org/2009/402.pdf

Download references

Author information

Authors and Affiliations

  1. Faculty of Science and Technology, Queensland University of Technology, Brisbane, QLD, Australia

    Leonie Simpson

  2. School of Mathematical and Geospatial Sciences, RMIT University, Melbourne, VIC, Australia

    Serdar Boztas

Authors
  1. Leonie Simpson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Serdar Boztas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Leonie Simpson.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Simpson, L., Boztas, S. State cycles, initialization and the Trivium stream cipher. Cryptogr. Commun. 4, 245–258 (2012). https://doi.org/10.1007/s12095-012-0066-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12095-012-0066-6

Keywords

Search

Navigation