Abstract
Previous work on program obfuscation gives strong negative results for general-purpose obfuscators, and positive results for obfuscating simple functions such as equality testing (point functions). In this work, we construct an obfuscator for a more complex algebraic functionality: testing for membership in a hyperplane (of constant dimension). We prove the security of the obfuscator under a new strong variant of the Decisional Diffie-Hellman assumption. Finally, we show a cryptographic application of the new obfuscator to digital signatures.
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-3-642-11799-2_36
Chapter PDF
Similar content being viewed by others
Keywords
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.
References
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)
Goldwasser, S., Rothblum, G.N.: On best-possible obfuscation. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 194–213. Springer, Heidelberg (2007)
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)
Hohenberger, S., Rothblum, G.N., Shelat, A., Vaikuntanathan, V.: Securely obfuscating re-encryption. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 233–252. Springer, Heidelberg (2007)
Goldwasser, S., Kalai, Y.T.: On the impossibility of obfuscation with auxiliary input. In: FOCS, pp. 553–562. IEEE Computer Society, Los Alamitos (2005)
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)
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)
Lynn, B.Y.S., 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)
Wee, H.: On obfuscating point functions. In: Proceedings of the 37th ACM Symposium on Theory of Computing, pp. 523–532 (2005)
Canetti, R., Dakdouk, R.R.: Obfuscating point functions with multibit output. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 489–508. Springer, Heidelberg (2008)
Dodis, Y., Smith, A.: Correcting errors without leaking partial information. In: STOC, pp. 654–663 (2005)
Adida, B., Wikström, D.: How to shuffle in public. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 555–574. Springer, Heidelberg (2007)
Shen, E., Shi, E., Waters, B.: Predicate privacy in encryption systems. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 457–473. Springer, Heidelberg (2009)
Hohenberger, S., Waters, B.: Short and stateless signatures from the rsa assumption. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 654–670. Springer, Heidelberg (2009)
Katz, J., Vaikuntanathan, V.: Signature schemes with bounded leakage resilience. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 703–720. Springer, Heidelberg (2009)
Canetti, R., Rothblum, G., Varia, M.: Obfuscation of hyperplane membership. Cryptology ePrint Archive (2009), http://eprint.iacr.org/
Canetti, R., Kalai, Y., Varia, M., Wichs, D.: On symmetric encryption and point obfuscation. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 52–71. Springer, Heidelberg (2010)
Krawczyk, H., Rabin, T.: Chameleon signatures. In: NDSS. The Internet Society (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Canetti, R., Rothblum, G.N., Varia, M. (2010). Obfuscation of Hyperplane Membership. In: Micciancio, D. (eds) Theory of Cryptography. TCC 2010. Lecture Notes in Computer Science, vol 5978. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11799-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-11799-2_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11798-5
Online ISBN: 978-3-642-11799-2
eBook Packages: Computer ScienceComputer Science (R0)