Advertisement

Shuffle and Mix: On the Diffusion of Randomness in Threshold Implementations of Keccak

  • Felix WegenerEmail author
  • Christian Baiker
  • Amir Moradi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11421)

Abstract

Threshold Implementations are well known as a provably first-order secure Boolean masking scheme even in the presence of glitches. A precondition for their security proof is a uniform input distribution at each round function, which may require an injection of fresh randomness or an increase in the number of shares. However, it is unclear whether violating the uniformity assumption causes detectable leakage in practice. Recently, Daemen undertook a theoretical study of lossy mappings to extend the understanding of uniformity violations. We complement his work by entropy simulations and practical measurements of Keccak’s round function. Our findings shed light on the necessity of mixing operations in addition to bit-permutations in a cipher’s linear layer to propagate randomness between S-boxes and prevent exploitable leakage. Finally, we argue that this result cannot be obtained by current simulation methods, further stressing the continued need for practical leakage measurements.

Notes

Acknowledgments

The work described in this paper has been supported in part by the German Federal Ministry of Education and Research BMBF (grant nr. 16KIS0666 SysKit_HW).

References

  1. 1.
    Side-channel AttacK User Reference Architecture. http://satoh.cs.uec.ac.jp/SAKURA/index.html
  2. 2.
    Arribas, V., Nikova, S., Rijmen, V.: VerMI: verification tool for masked implementations. IACR Cryptology ePrint Archive, 2017:1227 (2017)Google Scholar
  3. 3.
    Barthe, G., Belaïd, S., Fouque, P.-A., Grégoire, B.: maskVerif: a formal tool for analyzing software and hardware masked implementations. IACR Cryptology ePrint Archive, 2018:562 (2018)Google Scholar
  4. 4.
    Bertoni, G., Daemen, J., Peeters, M., Van Assche, G.: Keccak. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 313–314. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-38348-9_19CrossRefGoogle Scholar
  5. 5.
    Beyne, T., Bilgin, B.: Uniform first-order threshold implementations. In: Avanzi, R., Heys, H. (eds.) SAC 2016. LNCS, vol. 10532, pp. 79–98. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-69453-5_5CrossRefGoogle Scholar
  6. 6.
    Bilgin, B., Daemen, J., Nikov, V., Nikova, S., Rijmen, V., Van Assche, G.: Efficient and first-order DPA resistant implementations of Keccak. In: Francillon, A., Rohatgi, P. (eds.) CARDIS 2013. LNCS, vol. 8419, pp. 187–199. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-08302-5_13CrossRefGoogle Scholar
  7. 7.
    Bloem, R., Gross, H., Iusupov, R., Könighofer, B., Mangard, S., Winter, J.: Formal verification of masked hardware implementations in the presence of glitches. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10821, pp. 321–353. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-78375-8_11CrossRefzbMATHGoogle Scholar
  8. 8.
    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_31CrossRefGoogle Scholar
  9. 9.
    Daemen, J.: On non-uniformity in threshold sharings. In: Bilgin, B., Nikova, S., Rijmen, V. (eds.) Proceedings of the ACM Workshop on Theory of Implementation Security, TIS@CCS 2016, p. 41. ACM, New York (2016)CrossRefGoogle Scholar
  10. 10.
    Daemen, J.: Spectral characterization of iterating lossy mappings. In: Carlet, C., Hasan, M.A., Saraswat, V. (eds.) SPACE 2016. LNCS, vol. 10076, pp. 159–178. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-49445-6_9CrossRefGoogle Scholar
  11. 11.
    Daemen, J.: Changing of the guards: a simple and efficient method for achieving uniformity in threshold sharing. In: Fischer, W., Homma, N. (eds.) CHES 2017. LNCS, vol. 10529, pp. 137–153. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-66787-4_7CrossRefGoogle Scholar
  12. 12.
    Ishai, Y., Sahai, A., Wagner, D.: Private circuits: securing hardware against probing attacks. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 463–481. Springer, Heidelberg (2003).  https://doi.org/10.1007/978-3-540-45146-4_27CrossRefGoogle Scholar
  13. 13.
    Jungk, B., Apfelbeck, J.: Area-efficient FPGA implementations of the SHA-3 finalists. In: Athanas, P.M., Becker, J., Cumplido, R. (eds.) 2011 International Conference on Reconfigurable Computing and FPGAs, ReConFig 2011, pp. 235–241. IEEE Computer Society, Washington, D.C. (2011)CrossRefGoogle Scholar
  14. 14.
    Kocher, P., Jaffe, J., Jun, B.: Differential power analysis. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 388–397. Springer, Heidelberg (1999).  https://doi.org/10.1007/3-540-48405-1_25CrossRefGoogle Scholar
  15. 15.
    De Meyer, L., Bilgin, B., Reparaz, O.: Consolidating security notions in hardware masking. IACR Cryptology ePrint Archive, 2018:597 (2018)Google Scholar
  16. 16.
    Moradi, A., Richter, B., Schneider, T., Standaert, F.-X.: Leakage detection with the x2-test. IACR Trans. Cryptogr. Hardw. Embed. Syst. 2018(1), 209–237 (2018)Google Scholar
  17. 17.
    Nikova, S., Rechberger, C., Rijmen, V.: Threshold implementations against side-channel attacks and glitches. In: Ning, P., Qing, S., Li, N. (eds.) ICICS 2006. LNCS, vol. 4307, pp. 529–545. Springer, Heidelberg (2006).  https://doi.org/10.1007/11935308_38CrossRefzbMATHGoogle Scholar
  18. 18.
    National Institute of Standards and Technology: Sha-3 standard: permutation-based hash and extendable-output functions. FIPS Publikcation 2015:1–37 (2015)Google Scholar
  19. 19.
    Poschmann, A., Moradi, A., Khoo, K., Lim, C.-W., Wang, H., Ling, S.: Side-channel resistant crypto for less than 2, 300 GE. J. Cryptology 24(2), 322–345 (2011)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Reparaz, O., Bilgin, B., Nikova, S., Gierlichs, B., Verbauwhede, I.: Consolidating masking schemes. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9215, pp. 764–783. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-47989-6_37CrossRefGoogle Scholar
  21. 21.
    Schneider, T., Moradi, A.: Leakage assessment methodology. In: Güneysu, T., Handschuh, H. (eds.) CHES 2015. LNCS, vol. 9293, pp. 495–513. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-48324-4_25CrossRefGoogle Scholar
  22. 22.
    Wegener, F., Moradi, A.: A first-order SCA resistant AES without fresh randomness. In: Fan, J., Gierlichs, B. (eds.) COSADE 2018. LNCS, vol. 10815, pp. 245–262. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-89641-0_14CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Horst Görtz Institute for IT SecurityRuhr University BochumBochumGermany

Personalised recommendations