Abstract
This paper studies the security of blockciphers with generalized Feistel structures (GFS) consisting of SP-type F-functions. While GFS leads to compact implementations, the security is not well understood, in particular for larger values of the partitioning number which indicates the number of subblocks. For both differential and linear cryptanalysis, we first prove tighter lower bounds on the minimum number of active S-boxes for four and six rounds of the GFS utilizing word-based rotation as a round permutation. These bounds are almost twice as large as the previous results in literature. Then we present a new approach to derive the first tight lower bounds for the minimum number of active S-boxes in several types of GFS with large parameters. The proposed algorithm exploits word-based truncated differential search and three-round relations of Feistel connections. By applying our results, the number of rounds required to be secure against differential and linear attacks can be reduced significantly. Thus the results enable us to design a more efficient symmetric key primitive. Moreover, we show that the improved GFS proposed by Suzaki and Minematsu at FSE 2010 have more active S-boxes than the standard GFS.
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Shibutani, K. (2011). On the Diffusion of Generalized Feistel Structures Regarding Differential and Linear Cryptanalysis. In: Biryukov, A., Gong, G., Stinson, D.R. (eds) Selected Areas in Cryptography. SAC 2010. Lecture Notes in Computer Science, vol 6544. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19574-7_15
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DOI: https://doi.org/10.1007/978-3-642-19574-7_15
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