Abstract
In this paper we present the first multidimensional linear attack on \(\text {PRINCE}_{core}\), which uses an identical round-key for each round. Traditional one-dimensional and multidimensional linear cryptanalysis based their theoretical foundation on the independent-key assumption, so that they cannot be evaluated accurately in the case of ciphers with identical round-key. In this paper we propose a new classification technique to overcome this obstacle. In our new technique, we classify the linear trails into different subsets indexed by the XOR sum of their trail masks, deal with their correlations in each subset, and get the accurate capacity for our target linear approximation. By this technique, we build an 8-round multidimensional linear distinguisher with capacity of \(2^{-57.99}\), and exhibit a key-recovery attack on 9 out of 12 round of \(\text {PRINCE}_{core}\). This attack requires a data complexity of \(2^{63.84}\) known plaintexts and time complexity of \(2^{60}\) encryptions. We also present a key-recovery attack on 10-round \(\text {PRINCE}_{core}\) with data complexity of \(2^{63.84}\) known plaintexts and time complexity of \(2^{75.68}\) encryptions.
This work was supported by the National Basic Research Program of China (973 Project, No.2013CB338002), the National High Technology Research and Development Program of China (863 Program, No.2013AA014002), the IIE’s Cryptography Research Project (No.Y3Z0027103), and the Strategic Priority Research Program of Chinese Academy of Sciences under Grant XDA06010702.
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Eli, B., Shamir, A.: Differential cryptanalysis of DES-like cryptosystems. J. Cryptology 4(1), 3–72 (1991)
Matsui, M.: Linear cryptanalysis method for DES cipher. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 386–397. Springer, Heidelberg (1994)
Matsui, M.: The first experimental cryptanalysis of the data encryption standard. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 1–11. Springer, Heidelberg (1994)
Nyberg, K.: Linear approximation of block ciphers. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 439–444. Springer, Heidelberg (1995)
Hermelin, M., Nyberg, K.: Linear crypranalysis Using Multiple Linear Approximation. IACR Cryptology ePrint Archive 2011.93
Nyberg, K.: Correlation theorems in cryptanalysis. Discrete Appl. Math. 111(1), 177–188 (2001)
Daemen, J., Rijmen, V.: The Design of Rijndael: AES - The Advanced Encryption Standard. Information Security and Cryptography. Springer, Heidelberg (2002)
Hermelin, M., Nyberg, K.: Multidimensional linear distinguishing attacks and Boolean functions. In: Fourth International Workshop on Boolean Functions: Cryptography and Applications (2008)
Selçuk, A.A.: On probability of success in linear and differential cryptanalysis. J. Cryptology 21(1), 131–147 (2008)
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)
Hermelin, M., Nyberg, K.: Dependent linear approximations: the algorithm of Biryukov and others revisited. In: Pieprzyk, J. (ed.) CT-RSA 2010. LNCS, vol. 5985, pp. 318–333. Springer, Heidelberg (2010)
Hermelin, M.: Multidimensional linear cryptanalysis. Ph.D. thesis, Aalto University School of Science and Technology (2010)
Guo, J., Peyrin, T., Poschmann, A., Robshaw, M.: The LED block cipher. In: Preneel, B., Takagi, T. (eds.) CHES 2011. LNCS, vol. 6917, pp. 326–341. Springer, Heidelberg (2011)
Borghoff, J., Canteaut, A., Güneysu, T., Kavun, E.B., Knezevic, M., Knudsen, L.R., Leander, G., Nikov, V., Paar, C., Rechberger, C., Rombouts, P., Thomsen, S.S., Yalçın, T.: PRINCE – a low-latency block cipher for pervasive computing applications. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 208–225. Springer, Heidelberg (2012)
Blondeau, C., Nyberg, K.: New links between differential and linear cryptanalysis. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 388–404. Springer, Heidelberg (2013)
Hakala, R.M., Kivelä, A., Nyberg, K.: Estimating resistance against multidimensional linear attacks: an application on DEAN. In: Kutyłowski, M., Yung, M. (eds.) Inscrypt 2012. LNCS, vol. 7763, pp. 246–262. Springer, Heidelberg (2013)
Soleimany, H., Blondeau, C., Yu, X., Wu, W., Nyberg, K., Zhang, H., Zhang, L., Wang, Y.: Reflection cryptanalysis of PRINCE-like ciphers. In: Moriai, S. (ed.) FSE 2013. LNCS, vol. 8424, pp. 71–91. Springer, Heidelberg (2013)
Jean, J., Nikolić, I., Peyrin, T., Wang, L., Wu, S.: Security analysis of PRINCE. In: Moriai, S. (ed.) FSE 2013. LNCS, vol. 8424, pp. 92–111. Springer, Heidelberg (2013)
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Appendices
Appendix
A An Example of a Pattern Succession over 8-Round \(\text {PRINCE}_{core}\)
(See Fig. 3).
A pattern succession satisfying \(P_0=[0{\small *}00~0000~0000~0000], P_{8}=[{\small *}{\small *}0{\small *}~0000~0000~0000]\)
B Compute the Average Capacity for \(R\)-Round Key-Alternating Cipher
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Li, X., Li, B., Wu, W., Yu, X., Hao, R., Ma, B. (2014). First Multidimensional Cryptanalysis on Reduced-Round \(\mathrm{PRINCE }_{core}\) . In: Lee, HS., Han, DG. (eds) Information Security and Cryptology -- ICISC 2013. ICISC 2013. Lecture Notes in Computer Science(), vol 8565. Springer, Cham. https://doi.org/10.1007/978-3-319-12160-4_10
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DOI: https://doi.org/10.1007/978-3-319-12160-4_10
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