Abstract
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.
Work supported by NSF grants 0331548 and CFF-0635297, and BSF grant 2006317.
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Firefox password manager, http://www.firefoxtutor.com/61/securing-firefox-passwords/
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)
Bosley, C., Dodis, Y.: Does privacy require true randomness? In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, Springer, Heidelberg (2007)
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)
Dodis, Y., Spencer, J.: On the (non)universality of the one-time pad. In: 43rd Symposium on Foundations of Computer Science (2002)
Futoransky, A., Kargieman, E., Sarraute, C., Waissbein, A.: Foundations and applications for secure triggers. eprint, 284 (2005)
Goldreich, O., Levin, L.: Hard-core predicates for any one-way function. In: Proceedings of the 21st ACM symposium on Theory of computing (1989)
Goldwasser, S., Micali, S.: Probabilistic encryption. Journal of Computer and System Science 28, 270–299 (1984)
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)
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)
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)
Wee, H.: On obfuscating point functions. In: Proceedings of the 37th ACM symposium on Theory of computing, pp. 523–532 (2005)
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Canetti, R., Dakdouk, R.R. (2008). Obfuscating Point Functions with Multibit Output. In: Smart, N. (eds) Advances in Cryptology – EUROCRYPT 2008. EUROCRYPT 2008. Lecture Notes in Computer Science, vol 4965. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78967-3_28
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