Abstract
This paper describes a linearizing attack with fast calculus for higher order differential attack. The linearizing attack, proposed by Shimoyama et al. [13], [15], linearizes the attack equation and determines the key by Gaussian elimination. The cost of calculating the coefficient matrix is dominant overhead in this attack. We improve the algorithm used to calculate the coefficient matrix by applying a bit-slice type implementation [3]. We apply this method to five-round KASUMI and show that it need 227.5 chosen plaintexts and 234 KASUMI encryptions.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
3GPP TS 35202. 3rd Generation Partnership Project; Technical Specification Group Services and System Aspects; 3G Security; Specification of the 3GPP Confidentiality and Integrity Algorithms; Document 2: KASUMI Specification, http://www.3gpp.org/tb/other/algorithms.htm
Babbage, S., Frisch, L.: On MISTY1 higher order differential cryptanalysis. In: Won, D. (ed.) ICISC 2000. LNCS, vol. 2015, pp. 22–36. Springer, Heidelberg (2001)
Biham, E.: A Fast New DES Implementation in Software. In: Biham, E. (ed.) FSE 1997. LNCS, vol. 1267, pp. 260–272. Springer, Heidelberg (1997)
Biham, E., Shamir, A.: Differential Cryptanalysis of DES-Like Cryptosystems. Journal of Cryptology 4(1), 3–72 (1991)
Hatano, Y., Sekine, H., Kaneko, T.: Higher Order Differential Attack of Camellia (II). In: Nyberg, K., Heys, H.M. (eds.) SAC 2002. LNCS, vol. 2595, pp. 129–146. Springer, Heidelberg (2003)
Hatano, Y., Tanaka, H., Kaneko, T.: Optimization for the algebraic method and its application to an attack of MISTY1. IEIEC Trans. Fundamentals E87-A(1), 18–27 (2004)
Iwata, T., Kurosawa, K.: Probabilistic Higher Order Differential Attack and Higher Order Bent Functions. In: Lam, K.-Y., Okamoto, E., Xing, C. (eds.) ASIACRYPT 1999. LNCS, vol. 1716, pp. 62–74. Springer, Heidelberg (1999)
Jakobsen, T., Knudsen, L.R.: The Interpolation Attack on Block Cipher. In: Biham, E. (ed.) FSE 1997. LNCS, vol. 1267, pp. 28–40. Springer, Heidelberg (1997)
Knudsen, L.R., Wagner, D.: Integral Cryptanalysis. In: Daemen, J., Rijmen, V. (eds.) FSE 2002. LNCS, vol. 2365, pp. 112–127. Springer, Heidelberg (2002)
Lai, X.: Higher Order Derivatives and Differential Cryptanalysis. In: proceedings of Communications and Cryptography, pp. 227–233. Kluwer Academic Publishers, Dordrecht (1994)
Matsui, M.: New Block Encryption Algorithm MISTY. In: Biham, E. (ed.) FSE 1997. LNCS, vol. 1267, pp. 54–67. Springer, Heidelberg (1997)
Matsui, M.: Linear Cryptanalysis Method for DES Cipher. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 386–397. Springer, Heidelberg (1994)
Moriai, S., Shimoyama, T., Kaneko, T.: Higher Order Differential Attack of a CAST Cipher. In: Vaudenay, S. (ed.) FSE 1998. LNCS, vol. 1372, pp. 17–31. Springer, Heidelberg (1998)
Moriai, S., Shimoyama, T., Kaneko, T.: Higher Order Differential Attack Using Chosen Higher Order Differences. In: Tavares, S., Meijer, H. (eds.) SAC 1998. LNCS, vol. 1556, pp. 106–117. Springer, Heidelberg (1999)
Shimoyama, T., Moriai, S., Kaneko, T., Tsujii, S.: Improving Higher Order Differential Attack and Its Application to Nyberg-Knudesen’s Designed Block Cipher. IEIEC Trans. Fundamentals E82-A(9), 1971–1980 (1999)
Sugio, N., Tanaka, H., Kaneko, T.: A Study on Higher Order Differential Attack of KASUMI. In: proceedings of International Symposium on Information Theory and its Applications 2002, pp. 755–758 (2002)
Tanaka, H., Hisamatsu, K., Kaneko, T.: Strength of MISTY1 without FL Function for Higher Order Differential Attack. In: Fossorier, M.P.C., Imai, H., Lin, S., Poli, A. (eds.) AAECC 1999. LNCS, vol. 1719, pp. 221–230. Springer, Heidelberg (1999)
Tanakaü, H., Ishiiü, C.C., Kaneko, C.T.: On the Strength of KASUMI without FL Functions against Higher Order Differential Attack. In: Won, D. (ed.) ICISC 2000. LNCS, vol. 2015, pp. 14–21. Springer, Heidelberg (2001)
Tanakaü, H., Ishiiü, C.C., Kaneko, C.: On the strength of block cipher KASUMI and MISTY. In: Proceedings of Symposium on Cryptography and Information Security, pp. 647–652 (2001) (in Japanese)
Nambu, S., Kaneko, T.: A Study on Higher Order Differential Attack of KASUMI (III). In: Proceedings of The 27th Symposium on Information Theory and Its Applications, pp. 45–48 (2004) (in Japanese)
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
Sugio, N., Nambu, S., Kaneko, T. (2006). A Fast Calculus for the Linearizing Attack and Its Application to an Attack on KASUMI. In: Fossorier, M.P.C., Imai, H., Lin, S., Poli, A. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2006. Lecture Notes in Computer Science, vol 3857. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11617983_16
Download citation
DOI: https://doi.org/10.1007/11617983_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31423-3
Online ISBN: 978-3-540-31424-0
eBook Packages: Computer ScienceComputer Science (R0)