Abstract
Integral attacks belong to the classical attack vectors against any given block ciphers. However, providing arguments that a given cipher is resistant against those attacks is notoriously difficult. In this paper, based solely on the assumption of independent round keys, we develop significantly stronger arguments than what was possible before: our main result is that we show how to argue that the sum of ciphertexts over any possible subset of plaintext is key-dependent, i.e., the non existence of integral distinguishers.
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
Similar content being viewed by others
Notes
- 1.
- 2.
In the 11-round distinguisher shown in [11], each tweakey is not XORed to the full state. However, we confirmed that there are 11-round distinguishers even when each tweakey is XORed to the full state.
References
Baksi, A.: New insights on differential and linear bounds using mixed integer linear programming. In: Maimut, D., Oprina, A.-G., Sauveron, D. (eds.) SecITC 2020. LNCS, vol. 12596, pp. 41–54. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-69255-1_4
Banik, S., Pandey, S.K., Peyrin, T., Sasaki, Yu., Sim, S.M., Todo, Y.: GIFT: a small present. In: Fischer, W., Homma, N. (eds.) CHES 2017. LNCS, vol. 10529, pp. 321–345. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66787-4_16
Beaulieu, R., Shors, D., Smith, J., Treatman-Clark, S., Weeks, B., Wingers, L.: The SIMON and SPECK families of lightweight block ciphers. IACR Cryptol. ePrint Arch. 2013, 404 (2013)
Beierle, C., et al.: The SKINNY family of block ciphers and its low-latency variant MANTIS. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9815, pp. 123–153. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53008-5_5
Beierle, C., Leander, G., Moradi, A., Rasoolzadeh, S.: CRAFT: lightweight tweakable block cipher with efficient protection against DFA attacks. IACR Trans. Symmetric Cryptol. 2019(1), 5–45 (2019). https://doi.org/10.13154/tosc.v2019.i1.5-45
Bogdanov, A., et al.: PRESENT: an ultra-lightweight block cipher. In: Paillier, P., Verbauwhede, I. (eds.) CHES 2007. LNCS, vol. 4727, pp. 450–466. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74735-2_31
Boura, C., Canteaut, A.: Another view of the division property. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9814, pp. 654–682. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53018-4_24
Canteaut, A., Lallemand, V., Leander, G., Neumann, P., Wiemer, F.: bison instantiating the whitened swap-or-not construction. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019. LNCS, vol. 11478, pp. 585–616. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17659-4_20
Carlet, C., Crama, Y., Hammer, P.L.: Vectorial Boolean functions for cryptography. In: Crama, Y., Hammer, P.L. (eds.) Boolean Models and Methods in Mathematics, Computer Science, and Engineering, pp. 398–470. Cambridge University Press (2010). https://doi.org/10.1017/cbo9780511780448.012
Daemen, J., Knudsen, L., Rijmen, V.: The block cipher square. In: Biham, E. (ed.) FSE 1997. LNCS, vol. 1267, pp. 149–165. Springer, Heidelberg (1997). https://doi.org/10.1007/BFb0052343
Derbez, P., Fouque, P.: Increasing precision of division property. IACR Trans. Symmetric Cryptol. 2020(4), 173–194 (2020). https://doi.org/10.46586/tosc.v2020.i4.173-194
Hebborn, P., Lambin, B., Leander, G., Todo, Y.: Lower bounds on the degree of block ciphers. In: Moriai, S., Wang, H. (eds.) ASIACRYPT 2020. LNCS, vol. 12491, pp. 537–566. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64837-4_18
Jean, J.: TikZ for cryptographers (2016). https://www.iacr.org/authors/tikz/
Knudsen, L.R.: Truncated and higher order differentials. In: Preneel, B. (ed.) FSE 1994. LNCS, vol. 1008, pp. 196–211. Springer, Heidelberg (1995). https://doi.org/10.1007/3-540-60590-8_16
Lai, X.: Higher order derivatives and differential cryptanalysis. In: Blahut, R.E., Costello, D.J., Maurer, U., Mittelholzer, T. (eds.) Communications and Cryptography. The Springer International Series in Engineering and Computer Science (Communications and Information Theory), vol. 276. Springer, Boston (1994). https://doi.org/10.1007/978-1-4615-2694-0_23
Lai, X., Massey, J.L., Murphy, S.: Markov ciphers and differential cryptanalysis. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 17–38. Springer, Heidelberg (1991). https://doi.org/10.1007/3-540-46416-6_2
Lambin, B., Derbez, P., Fouque, P.-A.: Linearly equivalent S-boxes and the division property. Des. Codes Crypt. 88(10), 2207–2231 (2020). https://doi.org/10.1007/s10623-020-00773-4
Nyberg, K., Knudsen, L.R.: Provable security against a differential attack. J. Cryptol. 8(1), 27–37 (1995). https://doi.org/10.1007/BF00204800
Shibayama, N., Kaneko, T.: A new higher order differential of CLEFIA. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. 97–A(1), 118–126 (2014). https://doi.org/10.1587/transfun.E97.A.118
Todo, Y.: Structural evaluation by generalized integral property. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 287–314. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46800-5_12
Todo, Y., Morii, M.: Bit-based division property and application to Simon family. In: Peyrin, T. (ed.) FSE 2016. LNCS, vol. 9783, pp. 357–377. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-52993-5_18
Wang, Q., Liu, Z., Varıcı, K., Sasaki, Yu., Rijmen, V., Todo, Y.: Cryptanalysis of reduced-round SIMON32 and SIMON48. In: Meier, W., Mukhopadhyay, D. (eds.) INDOCRYPT 2014. LNCS, vol. 8885, pp. 143–160. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-13039-2_9
Xiang, Z., Zhang, W., Bao, Z., Lin, D.: Applying MILP method to searching integral distinguishers based on division property for 6 lightweight block ciphers. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10031, pp. 648–678. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53887-6_24
Yang, G., Zhu, B., Suder, V., Aagaard, M.D., Gong, G.: The Simeck family of lightweight block ciphers. IACR Cryptol. ePrint Arch. 2015, 612 (2015)
Acknowledgments
This work was partially funded by the DFG, (German Research Foundation) under Germany’s Excellence Strategy - EXC 2092 CASA – 390781972 and within the project Analysis and Protection of Lightweight Cryptographic Algorithms (432878529).
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 International Association for Cryptologic Research
About this paper
Cite this paper
Hebborn, P., Lambin, B., Leander, G., Todo, Y. (2021). Strong and Tight Security Guarantees Against Integral Distinguishers. In: Tibouchi, M., Wang, H. (eds) Advances in Cryptology – ASIACRYPT 2021. ASIACRYPT 2021. Lecture Notes in Computer Science(), vol 13090. Springer, Cham. https://doi.org/10.1007/978-3-030-92062-3_13
Download citation
DOI: https://doi.org/10.1007/978-3-030-92062-3_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-92061-6
Online ISBN: 978-3-030-92062-3
eBook Packages: Computer ScienceComputer Science (R0)