Skip to main content

On Fibonacci keystream generators

Session 8: Recent Results

Part of the Lecture Notes in Computer Science book series (LNCS,volume 1008)

Abstract

A number of keystream generators have been proposed which are based on Fibonacci sequences, and at least one has been fielded. They are attractive in that they can use some of the security results from the theory of shift register based keystream generators, while running much more quickly in software. However, new designs bring new risks, and we show how a system proposed at last year's workshop, the Fibonacci Shrinking Genertor (FISH), can be broken by an opponent who knows a few thousand words of keystream. We then discuss how such attacks can be avoided, and present a new algorithm, PIKE, which is based on the A5 algorithm used in GSM telephones.

References

  1. RA Rueppel, ‘Analysis and Design of Stream Ciphers', Springer Verlag Communications and Control Engineering Series (1986)

    Google Scholar 

  2. D Coppersmith, H Krawczyk, Y Mansour, “The Shrinking Generator”, in Advances in Cryptology — CRYPTO '93, Springer LNCS v 773 pp 22–39

    Google Scholar 

  3. H Krawczyk, “The Shrinking Generator: some practical considerations”, in Fast Software Encryption, Springer LNCS v 809 pp 45–46

    Google Scholar 

  4. DJ Wheeler, “A Bulk Data Encryption Algorithm”, in Fast Software Encryption, Springer LNCS v 809 pp 126–134

    Google Scholar 

  5. P Rogaway, D Coppersmith, “A Software-Optimised Encryption Algorithm”, in Fast Software Encryption, Springer LNCS v 809 pp 56–63

    Google Scholar 

  6. U Blöcher, M Dichtl, “Fish: a fast software stream cipher”, in Fast Software Encryption, Springer LNCS v 809 pp 41–44

    Google Scholar 

  7. JD Golić, “Linear Cryptanalysis of Stream Ciphers”, this volume

    Google Scholar 

  8. RP Brent, “On the periods of generalised Fibonacci sequences”, in Mathematics of Computation v 63 no 207 (July 1994) pp 389–401

    Google Scholar 

  9. RJ Anderson, “Solving a Class of Stream Ciphers”, in Cryptologia v XIV no 3 (July 1990) pp 285–288

    Google Scholar 

  10. W Meier, O Staffelbach, “Fast Correlation Attacks on Certain Stream Ciphers”, in Journal of Cryptology v 1 (1989) pp 159–176

    Google Scholar 

  11. DJC MacKay, ‘A Free Energy Minimization Framework for Inference Problems in Modulo 2 Arithmetic” in this volume pp 179–195

    Google Scholar 

  12. TR Cain, AT Sherman, “How to break Gifford's Cipher”, in Proceedings of the 2nd ACM Conference on Computer and Communications Security (Fairfax, 1994) pp 198–209

    Google Scholar 

  13. RJ Anderson, “A5 (Was: HACKING DIGITAL PHONES)”, message number 〈2ts9a0$95r@lyra.csx.cam.ac.uk〉 posted to usenet newsgroup sci.crypt, 17 Jun 1994 13:43:28 GMT.

    Google Scholar 

  14. M Roe, private communication

    Google Scholar 

  15. WG Chambers, “On Random Mappings and Random Permutations”, this volume pp 22–28

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Anderson, R. (1995). On Fibonacci keystream generators. In: Preneel, B. (eds) Fast Software Encryption. FSE 1994. Lecture Notes in Computer Science, vol 1008. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60590-8_26

Download citation

  • DOI: https://doi.org/10.1007/3-540-60590-8_26

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60590-4

  • Online ISBN: 978-3-540-47809-6

  • eBook Packages: Springer Book Archive