Abstract
SPECK is a lightweight block cipher family designed by the U.S. National Security Agency and published in 2013. Although several cryptanalyses have been applied since then, no linear results have been proposed. In this paper, we apply Wallén’s enumeration algorithm to Matsui’s branch-and-bound framework and find the best correlations of SPECK reduced to various rounds, i.e. full rounds of SPECK-32 and 7/ 5/ 4/ 4 rounds of SPECK-48/ 64/ 96/ 128. Since the best 10-round correlation of SPECK-32 is as small as \(2^{-17}\) already, SPECK-32 is immune to the 1-dimensional linear cryptanalysis. Moreover, we present several distinguishers and key recovery attacks as an application of the linear trails. Besides the search for linear trails, we also discuss possible implementations of the Wallén’s algorithm and provide an implementation which is faster than the straightforward implementations.
This work is supported by the National Basic Research Program of China (No. 2013CB338002).
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Notes
- 1.
This definition is the method proposed by Wallén to calculate the CPM.
References
Beaulieu, R., Shors, D., Smith, J., Treatman-Clark, S., Weeks, B., Wingers, L.: The SIMON and SPECK families of lightweight block ciphers. Cryptology ePrint Archive, Report 2013/404 (2013). http://eprint.iacr.org/
Biryukov, A., Velichkov, V.: Automatic search for differential trails in ARX ciphers. In: Benaloh, J. (ed.) CT-RSA 2014. LNCS, vol. 8366, pp. 227–250. Springer, Heidelberg (2014). http://dx.doi.org/10.1007/978-3-319-04852-9_12
Cho, J.Y., Hermelin, M.: Improved linear cryptanalysis of SOSEMANUK. In: Lee, D., Hong, S. (eds.) ICISC 2009. LNCS, vol. 5984, pp. 101–117. Springer, Heidelberg (2010). http://dx.doi.org/10.1007/978-3-642-14423-3_8
Dinur, I.: Improved differential cryptanalysis of round-reduced SPECK. Cryptology ePrint Archive, Report 2014/320 (2014). http://eprint.iacr.org/. Accepted by SAC 2014
Hermelin, M.: Multidimensional Linear Cryptanalysis. Ph.D. thesis, Aalto University School of Science and Technology, Faculty of Information and Natural Sciences, Department of Information and Computer Science (2003). http://lib.tkk.fi/Diss/2010/isbn9789526031903/isbn9789526031903.pdf
Hermelin, M., Cho, J.Y., Nyberg, K.: Multidimensional extension of matsui’s algorithm 2. In: Dunkelman, O. (ed.) FSE 2009. LNCS, vol. 5665, pp. 209–227. Springer, Heidelberg (2009). http://dx.doi.org/10.1007/978-3-642-03317-9_13
Knuth, D.: The Art of Computer Programming: Generating All Tuples and Permutations. Addison-Wesley Series in Computer Science and Information Proceedings, vol. 4. Addison Wesley Publishing Company Incorporated, Upper Saddle River (2005)
Matsui, M.: On correlation between the order of S-Boxes and the strength of DES. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 366–375. Springer, Heidelberg (1995). http://dx.doi.org/10.1007/BFb0053451
Nyberg, K., Wallén, J.: Improved linear distinguishers for SNOW 2.0. In: Robshaw, M. (ed.) FSE 2006. LNCS, vol. 4047, pp. 144–162. Springer, Heidelberg (2006). http://dx.doi.org/10.1007/11799313_10
Wallén, J.: Linear approximations of addition modulo 2\(^{n}\). In: Johansson, T. (ed.) FSE 2003. LNCS, vol. 2887, pp. 261–273. Springer, Heidelberg (2003). http://dx.doi.org/10.1007/978-3-540-39887-5_20
Wallén, J.: On the differential and linear properties of addition. Master’s thesis, Helsinki University of Technology, Department of Computer Science and Engineering, Laboratory for Theoretical Computer Science (2003). http://www.tcs.hut.fi/Publications/bibdb/HUT-TCS-A84.pdf
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Appendices
A Straightforward Implementations of Wallén’s Algorithm
The mode argument indicates whether \(\varvec{u},\varvec{v},\varvec{w}\) are fixed and used hereafter.
1.1 A.1 The Top-Down Method
1.2 A.2 The Bottom-Up Method
B The Gray_Visit Procedure
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Yao, Y., Zhang, B., Wu, W. (2015). Automatic Search for Linear Trails of the SPECK Family. In: Lopez, J., Mitchell, C. (eds) Information Security. ISC 2015. Lecture Notes in Computer Science(), vol 9290. Springer, Cham. https://doi.org/10.1007/978-3-319-23318-5_9
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DOI: https://doi.org/10.1007/978-3-319-23318-5_9
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