### On Virtual Grey Box Obfuscation for General Circuits

Nir Bitansky, Ran Canetti, Yael Tauman-Kalai, and Omer Paneth

##### Abstract

An obfuscator $\O$ is Virtual Grey Box (VGB) for a class $\C$ of circuits if, for any $C\in\C$ and any predicate $\pi$, deducing $\pi(C)$ given $\O(C)$ is tantamount to deducing $\pi(C)$ given unbounded computational resources and polynomially many oracle queries to $C$. VGB obfuscation is often significantly more meaningful than indistinguishability obfuscation (IO). In fact, for some circuit families of interest VGB is equivalent to full-fledged Virtual Black Box obfuscation. We investigate the feasibility of obtaining VGB obfuscation for general circuits. We first formulate a natural strengthening of IO, called {\em strong IO} (SIO). Essentially, $\O$ is SIO for class $\C$ if $\O(C)\approx\O(C')$ whenever the pair $(C,C')$ is taken from a distribution over $\C$ where, for all $x$, $C(x)\neq C'(x)$ only with negligible probability. We then show that an obfuscator is VGB for a class $\C$ if and only if it is SIO for $\C$. This result is unconditional and holds for any $\C$. We also show that, for some circuit collections, SIO implies virtual black-box obfuscation. Finally, we formulate a slightly stronger variant of the semantic security property of graded encoding schemes [Pass-Seth-Telang Crypto 14], and show that existing obfuscators, such as the obfuscator of Barak et al. [Eurocrypt 14], are SIO for all circuits in NC$^1$, assuming that the underlying graded encoding scheme satisfies our variant of semantic security. {\em Put together, we obtain VGB obfuscation for all NC$^1$ circuits under assumptions that are almost the same as those used by Pass et al. to obtain IO for NC$^1$ circuits.} We also show that semantic security is in essence {\em necessary} for showing VGB obfuscation.

Note: Noted that a preliminary version appears in the proceedings of crypto.

Available format(s)
Publication info
A major revision of an IACR publication in CRYPTO 2014
Keywords
Contact author(s)
nirbitan @ tau ac il
History
2014-08-05: last of 2 revisions
See all versions
Short URL
https://ia.cr/2014/554

CC BY

BibTeX

@misc{cryptoeprint:2014/554,
author = {Nir Bitansky and Ran Canetti and Yael Tauman-Kalai and Omer Paneth},
title = {On Virtual Grey Box Obfuscation for General Circuits},
howpublished = {Cryptology ePrint Archive, Paper 2014/554},
year = {2014},
note = {\url{https://eprint.iacr.org/2014/554}},
url = {https://eprint.iacr.org/2014/554}
}

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