Abstract
Some features of Feistel structures have caused them to be considered as an efficient structure for design of block ciphers. Although several structures are proposed relied on Feistel structure, the type-II generalized Feistel structures (GFS) based on SP-functions are more prominent. Because of difference cancellation, which occurs in Feistel structures, their resistance against differential and linear attack is not as expected. In order to improve the immunity of Feistel structures against differential and linear attack, two methods are proposed. One of them is using multiple MDS matrices, and the other is using changing permutations of sub-blocks.
In this paper by using mixed-integer linear programming (MILP) and summation representation method, a technique to count the active S-boxes is proposed. Moreover in some cases, the results proposed by Shibutani at SAC 2010 are improved. Also multiple MDS matrices are applied to GFS, and by relying on a proposed approach, the new inequalities related to using multiple MDS matrices are extracted, and results of using the multiple MDS matrices in type II GFS are evaluated. Finally results related to linear cryptanalysis are presented. Our results show that using multiple MDS matrices leads to \(22\%\) and \(19\%\) improvement in differential cryptanalysis of standard and improved 8 sub-blocks structures, respectively, after 18 rounds.
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 subscriptionsReferences
Aoki, K., et al.: Camellia: a 128-bit block cipher suitable for multiple platforms — design and analysis. In: Stinson, D.R., Tavares, S. (eds.) SAC 2000. LNCS, vol. 2012, pp. 39–56. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44983-3_4
Beierle, C., et al.: The SKINNY family of block ciphers and its low-latency variant MANTIS. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016, Part II. LNCS, vol. 9815, pp. 123–153. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53008-5_5
Bogdanov, A.: On unbalanced feistel networks with contracting MDS diffusion. Des. Codes Crypt. 59(1), 3558 (2011)
IBM: IBM ILOG CPLEX Optimizer. http://www.ibm.com/software/integration/optimization/cplex-optimizer/
Kanda, M.: Practical security evaluation against differential and linear cryptanalyses for feistel ciphers with SPN round function. In: Stinson, D.R., Tavares, S. (eds.) SAC 2000. LNCS, vol. 2012, pp. 324–338. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44983-3_24
Mouha, N., Wang, Q., Gu, D., Preneel, B.: Differential and linear cryptanalysis using mixed-integer linear programming. In: Wu, C.-K., Yung, M., Lin, D. (eds.) Inscrypt 2011. LNCS, vol. 7537, pp. 57–76. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34704-7_5
Sajadieh, M., Mirzaei, A., Mala, H., Rijmen, V.: A new counting method to bound the number of active s-boxes in Rijndael and 3D. Des. Codes Crypt. 83(2), 327–343 (2017)
Shibutani, K.: On the diffusion of generalized feistel structures regarding differential and linear cryptanalysis. In: Biryukov, A., Gong, G., Stinson, D.R. (eds.) SAC 2010. LNCS, vol. 6544, pp. 211–228. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19574-7_15
Shirai, T., Araki, K.: On generalized feistel structures using the diffusion switching mechanism. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E91-A(8), 2120–2129 (2008)
Shirai, T., Kanamaru, S., Abe, G.: Improved upper bounds of differential and linear characteristic probability for camellia. In: Daemen, J., Rijmen, V. (eds.) FSE 2002. LNCS, vol. 2365, pp. 128–142. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45661-9_10
Shirai, T., Shibutani, K.: Improving immunity of feistel ciphers against differential cryptanalysis by using multiple MDS matrices. In: Roy, B., Meier, W. (eds.) FSE 2004. LNCS, vol. 3017, pp. 260–278. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-25937-4_17
Shirai, T., Shibutani, K.: On feistel structures using a diffusion switching mechanism. In: Robshaw, M. (ed.) FSE 2006. LNCS, vol. 4047, pp. 41–56. Springer, Heidelberg (2006). https://doi.org/10.1007/11799313_4
Shirai, T., Shibutani, K., Akishita, T., Moriai, S., Iwata, T.: The 128-Bit blockcipher CLEFIA (Extended Abstract). In: Biryukov, A. (ed.) FSE 2007. LNCS, vol. 4593, pp. 181–195. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74619-5_12
Suzaki, T., Minematsu, K.: Improving the generalized feistel. In: Hong, S., Iwata, T. (eds.) FSE 2010. LNCS, vol. 6147, pp. 19–39. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13858-4_2
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Sajadieh, M., Vaziri, M. (2018). Using MILP in Analysis of Feistel Structures and Improving Type II GFS by Switching Mechanism. In: Chakraborty, D., Iwata, T. (eds) Progress in Cryptology – INDOCRYPT 2018. INDOCRYPT 2018. Lecture Notes in Computer Science(), vol 11356. Springer, Cham. https://doi.org/10.1007/978-3-030-05378-9_15
Download citation
DOI: https://doi.org/10.1007/978-3-030-05378-9_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-05377-2
Online ISBN: 978-3-030-05378-9
eBook Packages: Computer ScienceComputer Science (R0)