Protecting Obfuscation against Algebraic Attacks

  • Boaz Barak
  • Sanjam Garg
  • Yael Tauman Kalai
  • Omer Paneth
  • Amit Sahai
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8441)


Recently, Garg, Gentry, Halevi, Raykova, Sahai, and Waters (FOCS 2013) constructed a general-purpose obfuscating compiler for NC1 circuits. We describe a simplified variant of this compiler, and prove that it is a virtual black box obfuscator in a generic multilinear map model. This improves on Brakerski and Rothblum (eprint 2013) who gave such a result under a strengthening of the Exponential Time Hypothesis. We remove this assumption, and thus resolve an open question of Garg et al. As shown by Garg et al., a compiler for NC1 circuits can be bootstrapped to a compiler for all polynomial-sized circuits under the learning with errors (LWE) hardness assumption.

Our result shows that there is a candidate obfuscator that cannot be broken by algebraic attacks, hence reducing the task of creating secure obfuscators in the plain model to obtaining sufficiently strong security guarantees on candidate instantiations of multilinear maps.


Random Oracle Arithmetic Circuit Algebraic Attack Cryptology ePrint Archive Learning With Error 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Barak, B., Garg, S., Kalai, Y.T., Paneth, O., Sahai, A.: Protecting obfuscation against algebraic attacks. Cryptology ePrint Archive, Report 2013/631 (2013),
  2. 2.
    Barak, B., Goldreich, O., Impagliazzo, R., Rudich, S., Sahai, A., Vadhan, S.P., Yang, K.: On the (im)possibility of obfuscating programs. IACR Cryptology ePrint Archive 2001, 69 (2001)Google Scholar
  3. 3.
    Barrington, D.A.: Bounded-width polynomial-size branching programs recognize exactly those languages in nc 1. In: STOC (1986)Google Scholar
  4. 4.
    Brakerski, Z., Rothblum, G.N.: Virtual black-box obfuscation for all circuits via generic graded encoding. Cryptology ePrint Archive, Report 2013/563 (2013),
  5. 5.
    Canetti, R., Vaikuntanathan, V.: Obfuscating branching programs using black-box pseudo-free groups. Cryptology ePrint Archive (2013)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)CrossRefGoogle Scholar
  7. 7.
    Diffie, W., Hellman, M.E.: Multiuser cryptographic techniques. In: AFIPS National Computer Conference, pp. 109–112 (1976)Google Scholar
  8. 8.
    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)CrossRefGoogle Scholar
  9. 9.
    Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. Cryptology ePrint Archive, Report 2013/451 (2013),
  10. 10.
    Goyal, V., Ishai, Y., Sahai, A., Venkatesan, R., Wadia, A.: Founding cryptography on tamper-proof hardware tokens. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 308–326. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    Hada, S.: Zero-knowledge and code obfuscation. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 443–457. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  12. 12.
    Kilian, J.: Founding cryptography on oblivious transfer. In: Simon, J. (ed.) STOC, pp. 20–31. ACM (1988)Google Scholar

Copyright information

© International Association for Cryptologic Research 2014

Authors and Affiliations

  • Boaz Barak
    • 1
  • Sanjam Garg
    • 2
  • Yael Tauman Kalai
    • 1
  • Omer Paneth
    • 3
  • Amit Sahai
    • 4
  1. 1.Microsoft ResearchUSA
  2. 2.IBM ResearchUSA
  3. 3.Boston UniversityUSA
  4. 4.UCLAUSA

Personalised recommendations