Abstract
This work deals with the security and efficiency of type-I and type-II generalized Feistel networks (GFNs) with 4 lines. We propose to instantiate the GFNs with double SP-functions (substitution-permutation layer followed by another substitution-permutation layer) instead of single SP-functions (one substitution-permutation layer). We provide tight lower bounds on the number of differentially and linearly active functions and S-boxes in such ciphers. Based on these bounds, we show that the instantiation with double SP-functions using MDS diffusion has a proportion of differentially and linearly active S-boxes by up to 33% and 50% higher than that with single SP-functions for type-I and type-II GFNs, respectively. This opens up the possibility of designing more efficient block ciphers based on GFN structure. Note that type-I and type-II GFNs are the only non-contracting GFNs with 4 lines under a reasonable definition of a GFN.
A part of this work has been presented at the Seventh International Workshop on Coding and Cryptography in April 2011, Paris, France.
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.
Similar content being viewed by others
References
Bogdanov, A.: On the Differential and Linear Efficiency of Balanced Feistel Networks. Inf. Process. Lett. 110(20), 861–866 (2010)
Bogdanov, A.: On Unbalanced Feistel Networks with Contracting MDS Diffusion. Des. Codes Cryptography. Special issue: Coding and Cryptography 2009 (2010)
Daemen, J., Rijmen, V.: The Design of Rijndael: AES – The Advanced Encryption Standard. Springer, Heidelberg (2002)
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)
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)
Shirai, T., Araki, K.: On Generalized Feistel Structures Using the Diffusion Switching Mechanism. IEICE Transactions 91-A(8), 2120–2129 (2008)
Shirai, T., Preneel, B.: On Feistel Ciphers Using Optimal Diffusion Mappings Across Multiple Rounds. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 1–15. Springer, Heidelberg (2004)
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)
Shirai, T., Shibutani, K.: On Feistel Structures Using a Diffusion Switching Mechanism. In: Robshaw, M.J.B. (ed.) FSE 2006. LNCS, vol. 4047, pp. 41–56. Springer, Heidelberg (2006)
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)
Wu, W., Zhang, W., Lin, D.: Security on Generalized Feistel Scheme with SP Round Function. I. J. Network Security 3(3), 215–224 (2006)
Zheng, Y., Matsumoto, T., Imai, H.: On the Construction of Block Ciphers Provably Secure and Not Relying on Any Unproved Hypotheses. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 461–480. Springer, Heidelberg (1990)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bogdanov, A., Shibutani, K. (2011). Double SP-Functions: Enhanced Generalized Feistel Networks. In: Parampalli, U., Hawkes, P. (eds) Information Security and Privacy. ACISP 2011. Lecture Notes in Computer Science, vol 6812. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22497-3_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-22497-3_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22496-6
Online ISBN: 978-3-642-22497-3
eBook Packages: Computer ScienceComputer Science (R0)