Advertisement

Alzette: A 64-Bit ARX-box

(Feat. CRAX and TRAX)
Conference paper
  • 1.3k Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12172)

Abstract

S-boxes are the only source of non-linearity in many symmetric primitives. While they are often defined as being functions operating on a small space, some recent designs propose the use of much larger ones (e.g., 32 bits). In this context, an S-box is then defined as a subfunction whose cryptographic properties can be estimated precisely.

We present a 64-bit ARX-based S-box called Alzette, which can be evaluated in constant time using only 12 instructions on modern CPUs. Its parallel application can also leverage vector (SIMD) instructions. One iteration of Alzette has differential and linear properties comparable to those of the AES S-box, and two are at least as secure as the AES super S-box. As the state size is much larger than the typical 4 or 8 bits, the study of the relevant cryptographic properties of Alzette is not trivial.

We further discuss how such wide S-boxes could be used to construct round functions of 64-, 128- and 256-bit (tweakable) block ciphers with good cryptographic properties that are guaranteed even in the related-tweak setting. We use these structures to design a very lightweight 64-bit block cipher (Crax) which outperforms SPECK-64/128 for short messages on micro-controllers, and a 256-bit tweakable block cipher (Trax) which can be used to obtain strong security guarantees against powerful adversaries (nonce misuse, quantum attacks).

Keywords

(Tweakable) block cipher Related-tweak setting Long trail strategy Alzette MEDCP MELCC 

Notes

Acknowledgements

Part of the work of Christof Beierle was funded by Deutsche Forschungsgemeinschaft (DFG), project number 411879806, and part of the work of Christof Beierle was performed while he was at the University of Luxembourg and funded by the SnT CryptoLux RG budget. Luan Cardoso dos Santos is supported by the Luxembourg National Research Fund through grant PRIDE15/10621687/SPsquared. Part of the work of Aleksei Udovenko was performed while he was at the University of Luxembourg and funded by the Fonds National de la Recherche Luxembourg (project reference 9037104). Part of the work by Vesselin Velichkov was performed while he was at the University of Luxembourg. The work of Qingju Wang is funded by the University of Luxembourg Internal Research Project (IRP) FDISC. The experiments presented in this paper were carried out using the HPC facilities of the University of Luxembourg  [40] – see https://hpc.uni.lu.

References

  1. 1.
    AlTawy, R., et al.: SpoC: an authenticated cipher. NIST round 2 lightweight candidate (2019). https://csrc.nist.gov/CSRC/media/Projects/lightweight-cryptography/documents/round-2/spec-doc-rnd2/spoc-spec-round2.pdf
  2. 2.
    AlTawy, R., Gong, G., He, M., Mandal, K., Rohit, R.: SPIX: an authenticated cipher. NIST round 2 lightweight candidate (2019). https://csrc.nist.gov/CSRC/media/Projects/lightweight-cryptography/documents/round-2/spec-doc-rnd2/spix-spec-round2.pdf
  3. 3.
    AlTawy, R., Rohit, R., He, M., Mandal, K., Yang, G., Gong, G.: sLiSCP: Simeck-based permutations for lightweight sponge cryptographic primitives. In: Adams, C., Camenisch, J. (eds.) SAC 2017. LNCS, vol. 10719, pp. 129–150. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-72565-9_7CrossRefGoogle Scholar
  4. 4.
    Altawy, R., Rohit, R., He, M., Mandal, K., Yang, G., Gong, G.: SLISCP-light: towards hardware optimized sponge-specific cryptographic permutations. ACM Trans. Embed. Comput. Syst. 17(4), 81:1–81:26 (2018)CrossRefGoogle Scholar
  5. 5.
    Barreto, P., Nikov, V., Nikova, S., Rijmen, V., Tischhauser, E.: Whirlwind: a new cryptographic hash function. Des. Codes Cryptogr. 56(2), 141–162 (2010).  https://doi.org/10.1007/s10623-010-9391-yMathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Beaulieu, R., Shors, D., Smith, J., Treatman-Clark, S., Weeks, B., Wingers, L.: The SIMON and SPECK families of lightweight block ciphers. IACR Cryptology ePrint Archive 2013, 404 (2013). http://eprint.iacr.org/2013/404
  7. 7.
    Beaulieu, R., Shors, D., Smith, J., Treatman-Clark, S., Weeks, B., Wingers, L.: The SIMON and SPECK block ciphers on AVR 8-bit microcontrollers. Cryptology ePrint Archive, Report 2014/947 (2014). http://eprint.iacr.org/2014/947
  8. 8.
    Beierle, C., et al.: SCHWAEMM and ESCH: lightweight authenticated encryption and hashing using the Sparkle permutation family. NIST round 2 lightweight candidate (2019). https://csrc.nist.gov/CSRC/media/Projects/lightweight-cryptography/documents/round-2/spec-doc-rnd2/sparkle-spec-round2.pdf
  9. 9.
    Beierle, C., et al.: The SKINNY family of block ciphers and its low-latency variant MANTIS. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. Part II. LNCS, vol. 9815, pp. 123–153. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53008-5_5CrossRefGoogle Scholar
  10. 10.
    Beierle, C., et al.: SKINNY-AEAD and SKINNY-Hash. NIST round 2 lightweight candidate (2019). https://csrc.nist.gov/CSRC/media/Projects/lightweight-cryptography/documents/round-2/spec-doc-rnd2/SKINNY-spec-round2.pdf
  11. 11.
    Bernstein, D.J., et al.: Gimli: a cross-platform permutation. In: Fischer, W., Homma, N. (eds.) CHES 2017. LNCS, vol. 10529, pp. 299–320. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-66787-4_15CrossRefGoogle Scholar
  12. 12.
    Biham, E., Shamir, A.: Differential cryptanalysis of DES-like cryptosystems. In: Menezes, A.J., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 2–21. Springer, Heidelberg (1991).  https://doi.org/10.1007/3-540-38424-3_1CrossRefGoogle Scholar
  13. 13.
    Biryukov, A., De Cannière, C., Braeken, A., Preneel, B.: A toolbox for cryptanalysis: linear and affine equivalence algorithms. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 33–50. Springer, Heidelberg (2003).  https://doi.org/10.1007/3-540-39200-9_3CrossRefGoogle Scholar
  14. 14.
    Biryukov, A., Velichkov, V., Corre, Y.L.: Automatic search for the best trails in ARX: application to block cipher speck. In: Peyrin [34], pp. 289–310Google Scholar
  15. 15.
    Canteaut, A., et al.: Saturnin: a suite of lightweight symmetric algorithms for post-quantum security. NIST round 2 lightweight candidate (2019). https://csrc.nist.gov/CSRC/media/Projects/lightweight-cryptography/documents/round-2/spec-doc-rnd2/saturnin-spec-round2.pdf
  16. 16.
    Cheon, J.H., Takagi, T. (eds.): ASIACRYPT 2016. Part I. LNCS, vol. 10031. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53887-6CrossRefzbMATHGoogle Scholar
  17. 17.
    Dinu, D.: Efficient and secure implementations of lightweight symmetric cryptographic primitives. Ph.D. thesis, University of Luxembourg (2017). https://orbilu.uni.lu/handle/10993/33803
  18. 18.
    Dinu, D., Corre, Y.L., Khovratovich, D., Perrin, L., Großschädl, J., Biryukov, A.: Triathlon of lightweight block ciphers for the Internet of things. J. Cryptogr. Eng. 9(3), 283–302 (2018).  https://doi.org/10.1007/s13389-018-0193-x CrossRefGoogle Scholar
  19. 19.
    Dinu, D., Perrin, L., Udovenko, A., Velichkov, V., Großschädl, J., Biryukov, A.: Design strategies for ARX with provable bounds: Sparx and LAX. In: Cheon and Takagi [16], pp. 484–513Google Scholar
  20. 20.
    Fu, K., Wang, M., Guo, Y., Sun, S., Hu, L.: MILP-based automatic search algorithms for differential and linear trails for speck. In: Peyrin [34], pp. 268–288Google Scholar
  21. 21.
    Gueron, S., Johnson, S., Walker, J.: SHA-512/256. Cryptology ePrint Archive, Report 2010/548 (2010). http://eprint.iacr.org/2010/548
  22. 22.
    Gurobi Optimization, LLC: Gurobi optimizer reference manual (2018). http://www.gurobi.com
  23. 23.
    Knudsen, L.: Deal - a 128-bit block cipher. NIST AES Proposal (1998)Google Scholar
  24. 24.
    Kranz, T., Leander, G., Wiemer, F.: Linear cryptanalysis: key schedules and tweakable block ciphers. IACR Trans. Symmetric Cryptol. 2017(1), 474–505 (2017)Google Scholar
  25. 25.
    Krovetz, T., Rogaway, P.: The software performance of authenticated-encryption modes. In: Joux, A. (ed.) FSE 2011. LNCS, vol. 6733, pp. 306–327. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-21702-9_18CrossRefzbMATHGoogle Scholar
  26. 26.
    Leander, G., Abdelraheem, M.A., AlKhzaimi, H., Zenner, E.: A cryptanalysis of PRINTcipher: the invariant subspace attack. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 206–221. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-22792-9_12CrossRefGoogle Scholar
  27. 27.
    Liu, Y., Wang, Q., Rijmen, V.: Automatic search of linear trails in ARX with applications to SPECK and Chaskey. In: Manulis, M., Sadeghi, A.-R., Schneider, S. (eds.) ACNS 2016. LNCS, vol. 9696, pp. 485–499. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-39555-5_26CrossRefGoogle Scholar
  28. 28.
    Liu, Z.: Automatic tools for differential and linear cryptanalysis of ARX ciphers. Ph.D. thesis, University of Chinese Academy of Science (2017). (in Chinese)Google Scholar
  29. 29.
    Matsui, M.: Linear cryptanalysis method for DES cipher. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 386–397. Springer, Heidelberg (1994).  https://doi.org/10.1007/3-540-48285-7_33CrossRefGoogle Scholar
  30. 30.
    Matsui, M.: On correlation between the order of S-boxes and the strength of DES. In: Santis, A.D. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 366–375. Springer, Heidelberg (1995).  https://doi.org/10.1007/BFb0053451CrossRefGoogle Scholar
  31. 31.
    Niels, F., et al.: The Skein hash function family. Submission to the NIST SHA-3 competition (round 3) (2010)Google Scholar
  32. 32.
    Niemetz, A., Preiner, M., Biere, A.: Boolector 2.0 system description. J. Satisf. Boolean Model. Comput. 9, 53–58 (2014 (published 2015)). https://github.com/boolector/boolector
  33. 33.
    Patarin, J., Goubin, L., Courtois, N.: Improved algorithms for isomorphisms of polynomials. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 184–200. Springer, Heidelberg (1998).  https://doi.org/10.1007/BFb0054126CrossRefGoogle Scholar
  34. 34.
    Peyrin, T. (ed.): FSE 2016. LNCS, vol. 9783. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-52993-5CrossRefzbMATHGoogle Scholar
  35. 35.
    Peyrin, T., Seurin, Y.: Counter-in-tweak: authenticated encryption modes for tweakable block ciphers. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. Part I. LNCS, vol. 9814, pp. 33–63. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53018-4_2CrossRefzbMATHGoogle Scholar
  36. 36.
    Sun, L., Wang, W., Wang, M.: Automatic search of bit-based division property for ARX ciphers and word-based division property. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. Part I. LNCS, vol. 10624, pp. 128–157. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-70694-8_5CrossRefGoogle Scholar
  37. 37.
    Todo, Y.: Structural evaluation by generalized integral property. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. Part I. LNCS, vol. 9056, pp. 287–314. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-46800-5_12CrossRefGoogle Scholar
  38. 38.
    Todo, Y., Leander, G., Sasaki, Y.: Nonlinear invariant attack - practical attack on full SCREAM, iSCREAM, and Midori64. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. Part II. LNCS, vol. 10032, pp. 3–33. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53890-6_1CrossRefGoogle Scholar
  39. 39.
    Todo, Y., Morii, M.: Bit-based division property and application to Simon family. In: Peyrin [34], pp. 357–377Google Scholar
  40. 40.
    Varrette, S., Bouvry, P., Cartiaux, H., Georgatos, F.: Management of an academic HPC cluster: the UL experience. In: Proceedings of the 2014 International Conference on High Performance Computing & Simulation (HPCS 2014), pp. 959–967. IEEE, Bologna, July 2014Google Scholar
  41. 41.
    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 and Takagi [16], pp. 648–678Google Scholar

Copyright information

© International Association for Cryptologic Research 2020

Authors and Affiliations

  1. 1.Ruhr University BochumBochumGermany
  2. 2.University of LuxembourgEsch-sur-AlzetteLuxembourg
  3. 3.InriaParisFrance
  4. 4.CryptoExpertsParisFrance
  5. 5.University of EdinburghEdinburghUK

Personalised recommendations