Robust Pseudo-Random Number Generators with Input Secure Against Side-Channel Attacks

  • Michel Abdalla
  • Sonia Belaïd
  • David Pointcheval
  • Sylvain RuhaultEmail author
  • Damien Vergnaud
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9092)


A pseudo-random number generator (PRNG) is a deterministic algorithm that produces numbers whose distribution is indistinguishable from uniform. In this paper, we extend the formal model of PRNG with input defined by Dodis et al. at CCS 2013 to deal with partial leakage of sensitive information. The resulting security notion, termed leakage-resilient robust PRNG with input, encompasses all the previous notions, but also allows the adversary to continuously get some leakage on the manipulated data. Dodis et al. also proposed an efficient construction, based on simple operations in a finite field and a classical deterministic pseudo-random generator \(\mathbf {G}\). Here, we analyze this construction with respect to our new stronger security model, and prove that with a stronger \(\mathbf {G}\), it also resists leakage. We show that this stronger \(\mathbf {G}\) can be obtained by tweaking some existing constructions based on \(\mathsf {AES}\). We also propose a new instantiation which may be better in specific cases. Eventually, we show that the resulting scheme remains quite efficient in spite of its new security properties. It can thus be recommended in contexts where side-channel resistance is required.


Randomness Entropy Side-channel countermeasures Security models 



This research was supported in part by the French ANR-12-JS02-0004 ROMAnTIC Project and the French ANR-10-SEGI-015 PRINCE Project.


  1. 1.
    PolarSSL is an open source and commercial SSL library licensed by Offspark B.V.
  2. 2.
    Abdalla, M., Belaïd, S., Fouque, P.-A.: Leakage-resilient symmetric encryption via re-keying. In: Bertoni, G., Coron, J.-S. (eds.) CHES 2013. LNCS, vol. 8086, pp. 471–488. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  3. 3.
    Abdalla, M., Belaïd, S., Pointcheval, D., Ruhault, S., Vergnaud, D.: Robust pseudo-random number generators with input secure against side-channel attacks - full version. Cryptology ePrint Archive (2015)Google Scholar
  4. 4.
    Abdalla, M., Fouque, P.-A., Pointcheval, D.: Password-based authenticated key exchange in the three-party setting. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol. 3386, pp. 65–84. Springer, Heidelberg (2005) CrossRefGoogle Scholar
  5. 5.
    Aranha, D.F., Gouvêa, C.P.L.: RELIC is an Efficient LIbrary for Cryptography.
  6. 6.
    Barak, B., Halevi, S.: A model and architecture for pseudo-random generation with applications to /dev/random. In: Atluri, V., Meadows, C., Juels, A. (eds.) ACM CCS 05, pp. 203–212. ACM Press, November 2005Google Scholar
  7. 7.
    Belaïd, S., Grosso, V., Standaert, F.-X.: Masking and leakage-resilient primitives: one, the other(s) or both? Crypt. Commun. 7(1), 163–184 (2015)CrossRefGoogle Scholar
  8. 8.
    Bellare, M., Desai, A., Jokipii, E., Rogaway, P.: A concrete security treatment of symmetric encryption. In: 38th FOCS, pp. 394–403. IEEE Computer Society Press, October 1997Google Scholar
  9. 9.
    Bogdanov, A., Khovratovich, D., Rechberger, C.: Biclique cryptanalysis of the full AES. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 344–371. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  10. 10.
    Dodis, Y., Pointcheval, D., Ruhault, S., Vergnaud, D., Wichs, D.: Security analysis of pseudo-random number generators with input: /dev/random is not robust. In: Sadeghi, A.-R., Gligor, V.D., Yung, M. (eds.) ACM CCS 13, pp. 647–658. ACM Press, November 2013Google Scholar
  11. 11.
    Dodis, Y., Shamir, A., Stephens-Davidowitz, N., Wichs, D.: How to eat your entropy and have it too – optimal recovery strategies for compromised RNGs. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part II. LNCS, vol. 8617, pp. 37–54. Springer, Heidelberg (2014) Google Scholar
  12. 12.
    Duc, A., Dziembowski, S., Faust, S.: Unifying leakage models: from probing attacks to noisy leakage. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 423–440. Springer, Heidelberg (2014) CrossRefGoogle Scholar
  13. 13.
    Dziembowski, S., Pietrzak, K.: Leakage-resilient cryptography. In: 49th FOCS, pp. 293–302. IEEE Computer Society Press, October 2008Google Scholar
  14. 14.
    Faust, S., Kiltz, E., Pietrzak, K., Rothblum, G.N.: Leakage-resilient signatures. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 343–360. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  15. 15.
    Faust, S., Pietrzak, K., Schipper, J.: Practical leakage-resilient symmetric cryptography. In: Prouff, E., Schaumont, P. (eds.) CHES 2012. LNCS, vol. 7428, pp. 213–232. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  16. 16.
    Impagliazzo, R.: A personal view of average-case complexity. In: Structure in Complexity Theory Conference, pp. 134–147 (1995)Google Scholar
  17. 17.
    Lucks, S.: The sum of PRPs Is a secure PRF. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 470–484. Springer, Heidelberg (2000) CrossRefGoogle Scholar
  18. 18.
    Micali, S., Reyzin, L.: Physically observable cryptography. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 278–296. Springer, Heidelberg (2004) CrossRefGoogle Scholar
  19. 19.
    Pietrzak, K.: A leakage-resilient mode of operation. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 462–482. Springer, Heidelberg (2009) CrossRefGoogle Scholar
  20. 20.
    Prouff, E., Rivain, M.: Masking against side-channel attacks: a formal security proof. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 142–159. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  21. 21.
    Shoup, V.: A Computational Introduction to Number Theory and Algebra. Cambridge University Press, New York (2006)Google Scholar
  22. 22.
    Standaert, F.-X., Pereira, O., Yu, Y.: Leakage-resilient symmetric cryptography under empirically verifiable assumptions. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 335–352. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  23. 23.
    Veyrat-Charvillon, N., Gérard, B., Standaert, F.-X.: Soft analytical side-channel attacks. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8873, pp. 282–296. Springer, Heidelberg (2014) Google Scholar
  24. 24.
    Yu, Y., Standaert, F.-X., Pereira, O., Yung, M.: Practical leakage-resilient pseudorandom generators. In: Al-Shaer, E., Keromytis, A.D., Shmatikov, V. (eds.) ACM CCS 10, pp. 141–151. ACM Press, October 2010Google Scholar
  25. 25.
    Yu, Y., Standaert, F.-X.: Practical leakage-resilient pseudorandom objects with minimum public randomness. In: Dawson, E. (ed.) CT-RSA 2013. LNCS, vol. 7779, pp. 223–238. Springer, Heidelberg (2013) CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Michel Abdalla
    • 1
  • Sonia Belaïd
    • 1
    • 2
  • David Pointcheval
    • 1
  • Sylvain Ruhault
    • 1
    • 3
    Email author
  • Damien Vergnaud
    • 1
  1. 1.Ecole Normale Supérieure, CNRS, INRIA, and PSLParisFrance
  2. 2.Thales Communications and SecurityGennevilliersFrance
  3. 3.OppidaMontigny-le-BretonneuxFrance

Personalised recommendations