Abstract
Spectra attacks proposed recently are more data efficient than algebraic attacks against stream cipher. They are also time-and-space efficient. A measurement of the security of a stream cipher against spectra attacks is spectral immunity, the lowest spectral weight of the annihilator of the key stream. We study both the annihilator and the spectral immunity. We obtain a necessary and sufficient condition for the existence of low spectral weight annihilator and find it is more difficult to decide the (non)existence of the low weight annihilator for spectra attacks than for algebraic attacks. We also give some basic properties of annihilators and find the probability of a periodic sequence to be the annihilator of another sequence of the same period is low. Finally we prove that the spectral immunity is upper bounded by half of the period of the key stream. As a result, to recover any key stream, the least amount of bits required by spectra attacks is at most half of its period.
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.Z., Dawson, E., Henricksen, M., Simpson, L.: On the Security of the LILI Family of Stream Ciphers Against Algebraic Attacks. In: Pieprzyk, J., Ghodosi, H., Dawson, E. (eds.) ACISP 2007. LNCS, vol. 4586, pp. 11–28. Springer, Heidelberg (2007)
Billet, O., Gilbert, H.: Resistance of SNOW 2.0 Against Algebraic Attacks. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 19–28. Springer, Heidelberg (2005)
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)
Courtois, N.T.: 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)
Courtois, N.T.: 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. 345–359. Springer, Heidelberg (2003)
Du, Y., Pei, D.: Count of Annihilators of Boolean Functions with Given Algebraic Immunity. In: IEEE International Conference on Wireless Communications, Networking and Information Security (WCNIS), Beijing, China, pp. 640–643 (2010)
Gong, G., Ronjom, S., Helleseth, T., Hu, H.: Fast Discrete Fourier Spectra Attacks on Stream Ciphers. IEEE Trans. Inform. Theory 57(8), 5555–5565 (2011)
Golomb, S.W., Gong, G.: Signal Design for Good Correlation: For Wireless Communication, Cryptography and Radar. Cambridge University Press, Cambridge (2005)
Helleseth, T., Rønjom, S.: Simplifying Algebraic Attacks with Univariate Analysis. In: Information Theory and Applications Workshop (ITA), La Jolla, pp. 1–7 (2011)
Lidl, R., Niederreiter, H.: Finite Fields, Encyclopedia of Mathematics and its Applications, 2nd edn., vol. 20. Cambridge University Press, Cambridge (1997)
Meier, W., Pasalic, E., Carlet, C.: Algebraic Attacks and Decomposition of Boolean Functions. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 474–491. Springer, Heidelberg (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wang, J., Chen, K., Zhu, S. (2012). Annihilators of Fast Discrete Fourier Spectra Attacks. In: Hanaoka, G., Yamauchi, T. (eds) Advances in Information and Computer Security. IWSEC 2012. Lecture Notes in Computer Science, vol 7631. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34117-5_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-34117-5_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34116-8
Online ISBN: 978-3-642-34117-5
eBook Packages: Computer ScienceComputer Science (R0)