Abstract
In this paper, we mount the first algebraic attacks against clock controlled cascade stream ciphers. We first show how to obtain relations between the internal state bits and the output bits of the Gollmann clock controlled cascade stream ciphers. We demonstrate that the initial states of the last two shift registers can be determined by the initial states of the others. An alternative attack on the Gollmann cascade is also described, which requires solving quadratic equations. We then present an algebraic analysis of Pomaranch, one of the phase two proposals to eSTREAM. A system of equations of maximum degree four that describes the full cipher is derived. We also present weaknesses in the filter functions of Pomaranch by successfully computing annihilators and low degree multiples of the functions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Al-Hinai, S., Batten, L., Colbert, B., Wong, K.: Algebraic attacks on clock controlled stream ciphers. In: Batten, L.M., Safavi-Naini, R. (eds.) ACISP 2006. LNCS, vol. 4058, pp. 1–16. Springer, Heidelberg (2006)
Ars, G., Faugère, J.-C., Imai, H., Kawazoe, M., Sugita, M.: Comparison between XL and Gröbner basis algorithms. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 338–353. Springer, Heidelberg (2004)
Armknecht, F.: Improving fast algebraic attacks. In: Roy, B., Meier, W. (eds.) FSE 2004. LNCS, vol. 3017, pp. 65–82. Springer, Heidelberg (2004)
Armknecht, F., Krause, M.: Algebraic attacks on combiners with memory. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 162–175. Springer, Heidelberg (2003)
Chambers, W.G., Gollmann, D.: Lock-in Effect in Cascades of Clock-Controlled Shift-Registers. In: Günther, C.G. (ed.) EUROCRYPT 1988. LNCS, vol. 330, pp. 331–344. Springer, Heidelberg (1988)
Chambers, W.G.: Two stream ciphers. In: Anderson, R. (ed.) FSE 1993. LNCS, vol. 809, pp. 51–55. Springer, Heidelberg (1994)
Cho, J.Y., Pieprzyk, J.: Algebraic attacks on SOBER-t32 and SOBER-t16 without stuttering. In: Roy, B., Meier, W. (eds.) FSE 2004. LNCS, vol. 3017, pp. 49–64. Springer, Heidelberg (2004)
Cid, C., Gilbert, H., Johansson, T.: Cryptanalysis of Pomaranch. eSTREAM, ECRYPT Stream Cipher Project, Report 2005/060 (2005)
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)
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)
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)
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)
Courtois, N., Klimov, A., Patarin, J., Shamir, A.: Efficient algorithms for solving overdefined systems of multivariate polynomial equations. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 392–407. Springer, Heidelberg (2000)
Courtois, N., Patarin, J.: About the XL algorithm over GF(2). In: Joye, M. (ed.) CT-RSA 2003. LNCS, vol. 2612, pp. 141–157. Springer, Heidelberg (2003)
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)
Courtois, N., Debraize, B., Garrido, E.: On Exact Algebraic [Non-]Immunity of S-Boxes Based on Power Functions. In: Batten, L.M., Safavi-Naini, R. (eds.) ACISP 2006. LNCS, vol. 4058, pp. 76–86. Springer, Heidelberg (2006)
Gollmann, D.: Pseudo Random Properties of Cascade Connections of Clock Controlled Shift Registers. In: Beth, T., Cot, N., Ingemarsson, I. (eds.) EUROCRYPT 1984. LNCS, vol. 209, pp. 93–98. Springer, Heidelberg (1985)
Gollmann, D., Chambers, W.G.: Clock-controlled shift registers: a review. IEEE Journal on Selected Areas in Communications 7, 525–533 (1989)
Helleseth, T., Jansen, C., Kholosha, A.: Pomaranch - Design and Analysis of a Family of Stream Ciphers. eSTREAM, ECRYPT Stream Cipher Project, Report 2006/008 (2005)
Hasanzadeh, M., Khazaei, S., Kholosha, A.: On IV Setup of Pomaranch. eSTREAM, ECRYPT Stream Cipher Project, Report 2005/082 (2005)
Jansen, C., Helleseth, T., Kholosha, A.: Cascade Jump Controlled Sequence Generator and Pomaranch Stream Cipher (Version 3). eSTREAM, ECRYPT Stream Cipher Project, Report 2006/006 (2006)
Khazaei, S.: Cryptanalysis of Pomaranch (CJCSG). eSTREAM, ECRYPT Stream Cipher Project, Report 2005/065 (2005)
Menicocci, R.: Cryptanalysis of a two stage Gollmann cascade generator. In: Wolfowicz, W. (ed.) Proceedings of the 3rd Symposium on State and Progress of Research in Cryptography, pp. 62–69 (1993)
Park, S.J., Lee, S.J., Goh, S.C.: On the security of the Gollmann cascades. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 148–156. Springer, Heidelberg (1995)
Yang, B., Chen, J.: All in the XL Family: Theory and Practice. In: Park, C.-s., Chee, S. (eds.) ICISC 2004. LNCS, vol. 3506, pp. 67–86. Springer, Heidelberg (2005)
Zenner, E.: On the efficiency of the clock control guessing attack. In: Lee, P.J., Lim, C.H. (eds.) ICISC 2002. LNCS, vol. 2587, pp. 200–212. Springer, Heidelberg (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wong, K.KH., Colbert, B., Batten, L., Al-Hinai, S. (2006). Algebraic Attacks on Clock-Controlled Cascade Ciphers. In: Barua, R., Lange, T. (eds) Progress in Cryptology - INDOCRYPT 2006. INDOCRYPT 2006. Lecture Notes in Computer Science, vol 4329. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11941378_4
Download citation
DOI: https://doi.org/10.1007/11941378_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-49767-7
Online ISBN: 978-3-540-49769-1
eBook Packages: Computer ScienceComputer Science (R0)