Abstract
Calculating the distribution of certain functions during the linear cryptanalysis of stream ciphers is a frequently encountered problem. Let a function N (or a noise variable) be expressed via k mutually independent and uniformly distributed n-bit random variables X 1, X 2, ..., X k . The possibility to construct its distribution depends on the form of the expression N, and sometimes it becomes a bottleneck of the cryptanalysis.
In this paper we propose several new techniques to construct such distributions and widen the class of functions for which its distribution can efficiently be calculated.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Schneier, B.: Applied Cryptography: Protocols, Algorithms, and Source Code in C, 2nd edn. John Wiley&Sons, New York (1996)
Matsui, M.: Linear cryptanalysis method for DES cipher. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 386–397. Springer, Heidelberg (1994)
Halevi, S., Coppersmith, D., Jutla, C.S.: Scream: A software-efficient stream cipher. In: Daemen, J., Rijmen, V. (eds.) FSE 2002. LNCS, vol. 2365, pp. 195–209. Springer, Heidelberg (2002)
Ekdahl, P., Johansson, T.: A new version of the stream cipher SNOW. In: Nyberg, K., Heys, H.M. (eds.) SAC 2002. LNCS, vol. 2595, pp. 47–61. Springer, Heidelberg (2003)
Briceno, M., Goldberg, I., Wagner, D.: A pedagogical implementation of A5/1 (1999) (accessed August 18, 2003), available at http://jya.com/a51-pi.htm
SIG Bluetooth. Bluetooth specification (2003) (accessed August 18, 2003), available at http://www.bluetooth.com
Smart, N.: Cryptography: An Introduction. McGraw-Hill, New York (2003)
Hawkes, P., Rose, G.G.: Primitive specification and supporting documentation for SOBER-t16 submission to NESSIE. In: Proceedings of First Open NESSIE Workshop (2000) (accessed October 5, 2003) available at http://www.cryptonessie.org
Hawkes, P., Rose, G.G.: Primitive specification and supporting documentation for SOBER-t32 submission to NESSIE. In: Proceedings of First Open NESSIE Workshop (2000) (accessed October 5, 2003) available at http://www.cryptonessie.org
Watanabe, D., Biryukov, A., De Canniere, C.: A distinguishing attack of SNOW 2.0 with linear masking method. In: Matsui, M., Zuccherato, R.J. (eds.) SAC 2003. LNCS, vol. 3006, pp. 222–233. Springer, Heidelberg (2004)
Johansson, T., Maximov, A.: A linear distinguishing attack on Scream. In: Information Symposium in Information Theory—ISIT 2003, p. 164. IEEE Computer Society Press, Los Alamitos (2003)
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)
Maximov, A., Johansson, T., Babbage, S.: An improved correlation attack on A5/1. In: Handschuh, H., Hasan, M.A. (eds.) SAC 2004. LNCS, vol. 3357, pp. 1–18. Springer, Heidelberg (2004)
Fluhrer, S.R., McGrew, D.A.: Statistical analysis of the alleged RC4 keystream generator. In: Schneier, B. (ed.) FSE 2000. LNCS, vol. 1978, pp. 19–30. Springer, Heidelberg (2001)
Lu, Y., Vaudenay, S.: Cryptanalysis of bluetooth keystream generator two-level e0. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, Springer, Heidelberg (2004)
Ekdahl, P., Johansson, T.: Distinguishing attacks on SOBER-t16 and SOBER-t32. In: Daemen, J., Rijmen, V. (eds.) FSE 2002. LNCS, vol. 2365, pp. 210–224. Springer, Heidelberg (2002)
Lipmaa, H., Moriai, S.: Efficient algorithms for computing differential properties of addition. In: Matsui, M. (ed.) FSE 2001. LNCS, vol. 2355, pp. 336–350. Springer, Heidelberg (2002)
Lipmaa, H., Wallén, J., Dumas, P.: On the additive differential probability of exclusive-or. In: Roy, B., Meier, W. (eds.) FSE 2004. LNCS, vol. 3017, pp. 317–331. Springer, Heidelberg (2004)
Maximov, A.: On linear approximation of modulo sum. In: Roy, B., Meier, W. (eds.) FSE 2004. LNCS, vol. 3017, pp. 483–484. Springer, Heidelberg (2004)
Lipmaa, H.: On differential properties of pseudo-Hadamard transform and related mappings. In: Menezes, A.J., Sarkar, P. (eds.) INDOCRYPT 2002. LNCS, vol. 2551, pp. 48–61. Springer, Heidelberg (2002)
Maximov, A., Johansson, T.: Fast computation of large distributions and its cryptographic applications. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 313–332. Springer, Heidelberg (2005)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Maximov, A. (2007). On Large Distributions for Linear Cryptanalysis. In: Nam, KH., Rhee, G. (eds) Information Security and Cryptology - ICISC 2007. ICISC 2007. Lecture Notes in Computer Science, vol 4817. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76788-6_8
Download citation
DOI: https://doi.org/10.1007/978-3-540-76788-6_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-76787-9
Online ISBN: 978-3-540-76788-6
eBook Packages: Computer ScienceComputer Science (R0)