TY - GEN

T1 - On virtual grey box obfuscation for general circuits

AU - Bitansky, Nir

AU - Canetti, Ran

AU - Kalai, Yael Tauman

AU - Paneth, Omer

PY - 2014

Y1 - 2014

N2 - An obfuscator O is Virtual Grey Box (VGB) for a class C of circuits if, for any C ∈ C and any predicate π, deducing π(C) given O(C) is tantamount to deducing π(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 strong IO (SIO). Essentially, O is SIO for class C if O(C) ≈ O(C′) whenever the pair (C,C′) is taken from a distribution over C where, for all x, C(x) ≠ 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 NC1, assuming that the underlying graded encoding scheme satisfies our variant of semantic security. Put together, we obtain VGB obfuscation for all NC1 circuits under assumptions that are almost the same as those used by Pass et. al to obtain IO for NC1 circuits. We also show that semantic security is in essence necessary for showing VGB obfuscation.

AB - An obfuscator O is Virtual Grey Box (VGB) for a class C of circuits if, for any C ∈ C and any predicate π, deducing π(C) given O(C) is tantamount to deducing π(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 strong IO (SIO). Essentially, O is SIO for class C if O(C) ≈ O(C′) whenever the pair (C,C′) is taken from a distribution over C where, for all x, C(x) ≠ 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 NC1, assuming that the underlying graded encoding scheme satisfies our variant of semantic security. Put together, we obtain VGB obfuscation for all NC1 circuits under assumptions that are almost the same as those used by Pass et. al to obtain IO for NC1 circuits. We also show that semantic security is in essence necessary for showing VGB obfuscation.

UR - http://www.scopus.com/inward/record.url?scp=84905385071&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-44381-1_7

DO - 10.1007/978-3-662-44381-1_7

M3 - פרסום בספר כנס

AN - SCOPUS:84905385071

SN - 9783662443804

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 108

EP - 125

BT - Advances in Cryptology, CRYPTO 2014 - 34th Annual Cryptology Conference, Proceedings

PB - Springer Verlag

Y2 - 17 August 2014 through 21 August 2014

ER -