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Algorithms for Switching between Boolean and Arithmetic Masking of Second Order

  • Praveen Kumar Vadnala
  • Johann Großschädl
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8204)

Abstract

Masking is a widely-used countermeasure to thwart Differential Power Analysis (DPA) attacks, which, depending on the involved operations, can be either Boolean, arithmetic, or multiplicative. When used to protect a cryptographic algorithm that performs both Boolean and arithmetic operations, it is necessary to change the masks from one form to the other in order to be able to unmask the secret value at the end of the algorithm. To date, known techniques for conversion between Boolean and arithmetic masking can only resist first-order DPA. This paper presents the first solution to the problem of converting between Boolean and arithmetic masking of second order. To set the context, we show that a straightforward extension of first-order conversion schemes to second order is not possible. Then, we introduce two algorithms to convert from Boolean to arithmetic masking based on the second-order provably secure S-box output computation method proposed by Rivain et al (FSE 2008). The same can be used to obtain second-order secure arithmetic to Boolean masking. We prove the security of our conversion algorithms using similar arguments as Rivain et al. Finally, we provide implementation results of the algorithms on three different platforms.

Keywords

Differential power analysis Second-order DPA Arithmetic masking Boolean Masking Provably secure masking 

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References

  1. 1.
    Agrawal, D., Archambeault, B., Rao, J.R., Rohatgi, P.: The EM side-channel(s). In: Kaliski Jr., B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 29–45. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  2. 2.
    Chari, S., Jutla, C.S., Rao, J.R., Rohatgi, P.: Towards sound approaches to counteract power-analysis attacks. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 398–412. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  3. 3.
    Coron, J.-S., Giraud, C., Prouff, E., Renner, S., Rivain, M., Vadnala, P.K.: Conversion of security proofs from one leakage model to another: A new issue. In: Schindler, W., Huss, S.A. (eds.) COSADE 2012. LNCS, vol. 7275, pp. 69–81. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  4. 4.
    Coron, J.-S., Goubin, L.: On boolean and arithmetic masking against differential power analysis. In: Paar, C., Koç, Ç.K. (eds.) CHES 2000. LNCS, vol. 1965, pp. 231–237. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  5. 5.
    Coron, J.-S., Tchulkine, A.: A new algorithm for switching from arithmetic to boolean masking. In: Walter, C.D., Koç, Ç.K., Paar, C. (eds.) CHES 2003. LNCS, vol. 2779, pp. 89–97. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  6. 6.
    Debraize, B.: Efficient and provably secure methods for switching from arithmetic to boolean masking. In: Prouff, E., Schaumont, P. (eds.) CHES 2012. LNCS, vol. 7428, pp. 107–121. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  7. 7.
    Genelle, L., Prouff, E., Quisquater, M.: Secure multiplicative masking of power functions. In: Zhou, J., Yung, M. (eds.) ACNS 2010. LNCS, vol. 6123, pp. 200–217. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  8. 8.
    Genelle, L., Prouff, E., Quisquater, M.: Montgomery’s trick and fast implementation of masked AES. In: Nitaj, A., Pointcheval, D. (eds.) AFRICACRYPT 2011. LNCS, vol. 6737, pp. 153–169. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  9. 9.
    Genelle, L., Prouff, E., Quisquater, M.: Thwarting higher-order side channel analysis with additive and multiplicative maskings. In: Preneel, B., Takagi, T. (eds.) CHES 2011. LNCS, vol. 6917, pp. 240–255. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  10. 10.
    Goubin, L.: A sound method for switching between boolean and arithmetic masking. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, pp. 3–15. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  11. 11.
    Handschuh, H., Heys, H.M.: A timing attack on RC5. In: Tavares, S., Meijer, H. (eds.) SAC 1998. LNCS, vol. 1556, pp. 306–318. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  12. 12.
    Kelsey, J., Schneier, B., Wagner, D., Hall, C.: Side channel cryptanalysis of product ciphers. In: Quisquater, J.-J., Deswarte, Y., Meadows, C., Gollmann, D. (eds.) ESORICS 1998. LNCS, vol. 1485, pp. 97–110. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  13. 13.
    Kocher, P.C.: Timing Attacks on Implementations of Diffie-Hellman, RSA, DSS, and Other Systems. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 104–113. Springer, Heidelberg (1996)Google 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)CrossRefGoogle Scholar
  15. 15.
    Mangard, S., Oswald, M.E., Popp, T.: Power Analysis Attacks - Revealing the Secrets of Smart Cards, vol. 54, pp. 1–337. Springer (2007)Google Scholar
  16. 16.
    Messerges, T.S.: Using second-order power analysis to attack DPA resistant software. In: Paar, C., Koç, Ç.K. (eds.) CHES 2000. LNCS, vol. 1965, pp. 238–251. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  17. 17.
    Messerges, T.S.: Securing the AES finalists against power analysis attacks. In: Schneier, B. (ed.) FSE 2000. LNCS, vol. 1978, pp. 150–164. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  18. 18.
    Neiße, O., Pulkus, J.: Switching blindings with a view towards IDEA. In: Joye, M., Quisquater, J.-J. (eds.) CHES 2004. LNCS, vol. 3156, pp. 230–239. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  19. 19.
    Oswald, E., Mangard, S., Herbst, C., Tillich, S.: Practical second-order DPA attacks for masked smart card implementations of block ciphers. In: Pointcheval, D. (ed.) CT-RSA 2006. LNCS, vol. 3860, pp. 192–207. Springer, Heidelberg (2006), http://dx.doi.org/10.1007/11605805_13 CrossRefGoogle Scholar
  20. 20.
    Pan, J., Hartog, J.I., Lu, J.: You cannot hide behind the mask: Power analysis on a provably secure s-box implementation. In: Youm, H.Y., Yung, M. (eds.) WISA 2009. LNCS, vol. 5932, pp. 178–192. Springer, Heidelberg (2009), http://dx.doi.org/10.1007/978-3-642-10838-9_14 CrossRefGoogle Scholar
  21. 21.
    Rivain, M., Dottax, E., Prouff, E.: Block ciphers implementations provably secure against second order side channel analysis. In: Nyberg, K. (ed.) FSE 2008. LNCS, vol. 5086, pp. 127–143. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  22. 22.
    Tunstall, M., Whitnall, C., Oswald, E.: Masking tables—an underestimated security risk. In: Moriai, S. (ed.) Fast Software Encryption, 20th International Workshop, FSE 2013, Singapore, March 10-13. LNCS, Springer (2013) (Revised Selected Papers)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Praveen Kumar Vadnala
    • 1
  • Johann Großschädl
    • 1
  1. 1.Laboratory of Algorithmics, Cryptology and Security (LACS)University of LuxembourgLuxembourgLuxembourg

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