Obfuscating Point Functions with Multibit Output

  • Ran Canetti
  • Ronny Ramzi Dakdouk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4965)


We construct obfuscators of point functions with multibit output and other related functions. A point function with multibit output returns a fixed string on a single input point and zero everywhere else. Obfuscation of such functions has a useful application as a strong form of symmetric encryption which guarantees security even when the key has very low entropy: Essentially, learning information about the plaintext is paramount to finding the key via exhaustive search on the key space.

Although the constructions appear to be simple and modular, their analysis turns out to be quite intricate. In particular, we uncover some weaknesses in the current definitions of obfuscation. One weakness is that current definitions do not guarantee security even under very weak forms of composition. We thus define a notion of obfuscation that is preserved under an appropriate composition operation. The constructions can use any obfuscator of point functions under the proposed definition. Alternatively, they can use perfect one way (POW) functions with statistical indistinguishability, or with computational indistinguishability at the price of somewhat weaker security.


obfuscation composable obfuscation multibit point function obfuscation digital locker point function obfuscation 


  1. 1.
  2. 2.
    Barak, B., Goldreich, O., Impagliazzo, R., Rudich, S., Sahai, A., Vadhan, S., Yang, K.: On the (im)possibility of obfuscating programs. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 1–18. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  3. 3.
    Bosley, C., Dodis, Y.: Does privacy require true randomness? In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Canetti, R.: Towards realizing random oracles:hash functions that hide all partial information. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 455–469. Springer, Heidelberg (1997)Google Scholar
  5. 5.
    Canetti, R., Micciancio, D., Reingold, O.: Perfectly one-way probabilistic hash functions. In: Proceedings of the 30th ACM Symposium on Theory of Computing, pp. 131–140 (1998)Google Scholar
  6. 6.
    Dodis, Y., Spencer, J.: On the (non)universality of the one-time pad. In: 43rd Symposium on Foundations of Computer Science (2002)Google Scholar
  7. 7.
    Futoransky, A., Kargieman, E., Sarraute, C., Waissbein, A.: Foundations and applications for secure triggers. eprint, 284 (2005)Google Scholar
  8. 8.
    Goldreich, O., Levin, L.: Hard-core predicates for any one-way function. In: Proceedings of the 21st ACM symposium on Theory of computing (1989)Google Scholar
  9. 9.
    Goldwasser, S., Micali, S.: Probabilistic encryption. Journal of Computer and System Science 28, 270–299 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Hofheinz, D., Malone-Lee, J., Stam, M.: Obfuscation for cryptographic purposes. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 214–232. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  11. 11.
    Lynn, B., Prabhakaran, M., Sahai, A.: Positive results and techniques for obfuscation. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 20–39. Springer, Heidelberg (2004)Google Scholar
  12. 12.
    McInnes, J.L., Pinkas, B.: On the impossibility of private key cryptography with weakly random keys. In: Menezes, A., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 421–435. Springer, Heidelberg (1991)Google Scholar
  13. 13.
    Wee, H.: On obfuscating point functions. In: Proceedings of the 37th ACM symposium on Theory of computing, pp. 523–532 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Ran Canetti
    • 1
  • Ronny Ramzi Dakdouk
    • 2
  1. 1.IBM T. J. Watson Research Center, HawthorneNY
  2. 2.Yale UniversityNew Haven

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