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Zeroizing Without Low-Level Zeroes: New MMAP Attacks and their Limitations

  • Jean-Sébastien Coron
  • Craig Gentry
  • Shai Halevi
  • Tancrède Lepoint
  • Hemanta K. Maji
  • Eric Miles
  • Mariana Raykova
  • Amit Sahai
  • Mehdi Tibouchi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9215)

Abstract

We extend the recent zeroizing attacks of Cheon, Han, Lee, Ryu and Stehlé (Eurocrypt’15) on multilinear maps to settings where no encodings of zero below the maximal level are available. Some of the new attacks apply to the CLT13 scheme (resulting in a total break) while others apply to (a variant of) the GGH13 scheme (resulting in a weak-DL attack). We also note the limits of these zeroizing attacks.

Keywords

Cryptanalysis Hardness assumptions Multilinear maps 

References

  1. 1.
    Applebaum, B., Brakerski, Z.: Obfuscating circuits via composite-order graded encoding. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015, Part II. LNCS, vol. 9015, pp. 528–556. Springer, Heidelberg (2015). http://eprint.iacr.org/2015/025 Google Scholar
  2. 2.
    Barak, B., Garg, S., Kalai, Y.T., Paneth, O., Sahai, A.: Protecting obfuscation against algebraic attacks. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 221–238. Springer, Heidelberg (2014). http://dx.doi.org/10.1007/978-3-642-55220-5_13 CrossRefGoogle Scholar
  3. 3.
    Boneh, D., Wu, D.J., Zimmerman, J.: Immunizing multilinear maps against zeroizing attacks. Cryptology ePrint Archive, Report 2014/930 (2014). http://eprint.iacr.org/
  4. 4.
    Brakerski, Z., Rothblum, G.N.: Virtual black-box obfuscation for all circuits via generic graded encoding. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 1–25. Springer, Heidelberg (2014) CrossRefGoogle Scholar
  5. 5.
    Cheon, J.H., Han, K., Lee, C., Ryu, H., Stehlé, D.: Cryptanalysis of the multilinear map over the integers. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 3–12. Springer, Heidelberg (2015). http://eprint.iacr.org/2014/906 Google Scholar
  6. 6.
    Coron, J.-S., Lepoint, T., Tibouchi, M.: Practical multilinear maps over the integers. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 476–493. Springer, Heidelberg (2013). http://dx.doi.org/10.1007/978-3-642-40041-4_26 CrossRefGoogle Scholar
  7. 7.
    Garg, S., Gentry, C., Halevi, S.: Candidate multilinear maps from ideal lattices. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 1–17. Springer, Heidelberg (2013). http://dx.doi.org/10.1007/978-3-642-38348-9_1 CrossRefGoogle Scholar
  8. 8.
    Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: FOCS 2013, pp. 40–49. IEEE Computer Society (2013). http://doi.ieeecomputersociety.org/10.1109/FOCS.2013.13
  9. 9.
    Garg, S., Gentry, C., Halevi, S., Zhandry, M.: Fully secure functional encryption without obfuscation. Cryptology ePrint Archive, Report 2014/666 (2014). http://eprint.iacr.org/
  10. 10.
    Gentry, C., Lewko, A.B., Sahai, A., Waters, B.: Indistinguishability obfuscation from the multilinear subgroup elimination assumption. IACR Cryptology ePrint Archive 2014, 309 (2014). http://eprint.iacr.org/2014/309
  11. 11.
    Gentry, C., Lewko, A., Waters, B.: Witness encryption from instance independent assumptions. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part I. LNCS, vol. 8616, pp. 426–443. Springer, Heidelberg (2014). http://dx.doi.org/10.1007/978-3-662-44371-2_24 Google Scholar
  12. 12.
    Goldwasser, S., Micali, S.: Probabilistic encryption. J. Comput. Syst. Sci. 28(2), 270–299 (1984). http://dx.doi.org/10.1016/0022-0000(84)90070-9 MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Hansen, J.C., Schmutz, E.: How random is the characteristic polynomial of a random matrix? Math. Proc. Camb. Phi. Soc. 114, 507–515 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Hu, Y., Jia, H.: Cryptanalysis of GGH map. Cryptology ePrint Archive, Report 2015/301 (2015). http://eprint.iacr.org/
  15. 15.
    Kuba, G.: On the distribution of reducible polynomials. Math. Slovaca 59(3), 349–356 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Pass, R., Seth, K., Telang, S.: Indistinguishability obfuscation from semantically-secure multilinear encodings. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part I. LNCS, vol. 8616, pp. 500–517. Springer, Heidelberg (2014). http://dx.doi.org/10.1007/978-3-662-44371-2_28 Google Scholar
  17. 17.
    Zimmerman, J.: How to obfuscate programs directly. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 439–467. Springer, Heidelberg (2015). http://eprint.iacr.org/2014/776 Google Scholar

Copyright information

© International Association for Cryptologic Research 2015

Authors and Affiliations

  • Jean-Sébastien Coron
    • 1
  • Craig Gentry
    • 2
  • Shai Halevi
    • 2
  • Tancrède Lepoint
    • 3
  • Hemanta K. Maji
    • 4
    • 5
  • Eric Miles
    • 4
  • Mariana Raykova
    • 6
  • Amit Sahai
    • 4
  • Mehdi Tibouchi
    • 7
  1. 1.University of LuxembourgLuxembourgLuxembourg
  2. 2.IBM ResearchNew YorkUSA
  3. 3.CryptoExpertsParisFrance
  4. 4.Center for Encrypted FunctionalitiesUniversity of CaliforniaLos AngelesUSA
  5. 5.Purdue UniversityWest LafayetteUSA
  6. 6.SRI InternationalMenlo ParkUSA
  7. 7.NTT Secure Platform LaboratoriesTokyoJapan

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