Abstract
Matsui’s Algorithms 1 and 2 with multiple approximations have been studied over 16 years. In CRYPTO’04, Biryukov et al. proposed a formal framework based on m statistically independent approximations. Started by Hermelin et al. in ACISP’08, a different approach was taken by studying m-dimensional combined approximations from m base approximations. Known as multidimensional linear cryptanalysis, the requirement for statistical independence is relaxed. In this paper we study the multidimensional Alg. 1 of Hermelin et al.. We derive the formula for N, the number of samples required for the attack and we improve the algorithm by reducing time complexity of the distillation phase from 2m N to 2m2m + mN, and that of the analysis phase from 22m to 3m2m. We apply the results on 4- and 9-round Serpent and show that Hermelin et al. actually provided a formal model for the hypothesis of Biryukov et al. in practice, and this model is now much more practical with our improvements.
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
Biham, E., Dunkelman, O., Keller, N.: Linear Cryptanalysis of Reduced Round Serpent. In: Matsui, M. (ed.) FSE 2001. LNCS, vol. 2355, pp. 16–27. Springer, Heidelberg (2002)
Biryukov, A., De Cannière, C., Quisquater, M.: On Multiple Linear Approximations. In: Franklin, M. K. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 1–22. Springer, Heidelberg (2004)
Cho, J.Y., Hermelin, M., Nyberg, K.: A New Technique for Multidimensional Linear Cryptanalysis with Applications On Reduced Round Serpent. In: Lee, P.J., Cheon, J.H. (eds.) ICISC 2008. LNCS, vol. 5461, pp. 383–398. Springer, Heidelberg (2009)
Collard, B., Standaert, F.-X., Quisquater, J.-J.: Improved and Multiple Linear Cryptanalysis of Reduced Round Serpent. In: Pei, D., Yung, M., Lin, D., Wu, C. (eds.) Inscrypt 2007. LNCS, vol. 4990, pp. 51–65. Springer, Heidelberg (2008)
Collard, B., Standaert, F.-X., Quisquater, J.-J.: Improved and Multiple Linear Cryptanalysis of Reduced Round Serpent - Description of the Linear Approximations, 2007 (unpublished manuscript)
Collard, B., Standaert, F.-X., Quisquater, J.-J.: Improving the Time Complexity of Matsui’s Linear Cryptanalysis. In: Nam, K.-H., Rhee, G. (eds.) ICISC 2007. LNCS, vol. 4817, pp. 77–88. Springer, Heidelberg (2007)
Collard, B., Standaert, F.-X., Quisquater, J.-J.: Experiments on the Multiple Linear Cryptanalysis of Reduced Round Serpent. In: Nyberg, K. (ed.) FSE 2008. LNCS, vol. 5086, pp. 382–397. Springer, Heidelberg (2008)
Cormen, T.H., Stein, C., Rivest, R.L., Leiserson, C.E.: Introduction to Algorithms. McGraw-Hill Higher Education, New York (2001)
Desmedt, Y.G. (ed.): CRYPTO 1994. LNCS, vol. 839. Springer, Heidelberg (1994)
Hermelin, M., Cho, J.Y., Nyberg, K.: Multidimensional Linear Cryptanalysis of Reduced Round Serpent. In: Mu, Y., Susilo, W., Seberry, J. (eds.) ACISP 2008. LNCS, vol. 5107, pp. 203–215. Springer, Heidelberg (2008)
Kaliski Jr., B.S., Robshaw, M.J.B.: Linear Cryptanalysis Using Multiple Approximations. In: Desmedt (ed.) [9], pp. 26–39
Matsui, M.: Linear Cryptanalysis Method for DES Cipher. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 386–397. Springer, Heidelberg (1994)
Matsui, M.: The First Experimental Cryptanalysis of the Data Encryption Standard. In: Desmedt [9], pp. 1–11
Rao Yarlagadda, R.K., Hershey, J.E.: Hadamard Matrix Analysis and Synthesis: with Applications to Communications and Signal/image Processing. Kluwer Academic Publishers, Norwell (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nguyen, P.H., Wei, L., Wang, H., Ling, S. (2010). On Multidimensional Linear Cryptanalysis. In: Steinfeld, R., Hawkes, P. (eds) Information Security and Privacy. ACISP 2010. Lecture Notes in Computer Science, vol 6168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14081-5_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-14081-5_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14080-8
Online ISBN: 978-3-642-14081-5
eBook Packages: Computer ScienceComputer Science (R0)