- The (average case variants of the) notions of virtual black box obfuscation (Barak et al, CRYPTO '01) and virtual gray box obfuscation (Bitansky and Canetti, CRYPTO '10) coincide for evasive function families. We also define the notion of input-hiding obfuscation for evasive function families, stipulating that for a random c \in C it is hard to find, given O(c), a value outside the preimage of 0. Interestingly, this natural definition, also motivated by applications, is likely not implied by the seemingly stronger notion of average-case virtual black-box obfuscation.
- If there exist average-case virtual gray box obfuscators for all evasive function families, then there exist (quantitatively weaker) average-case virtual gray obfuscators for all function families.
- There does not exist a worst-case virtual black box obfuscator even for evasive circuits, nor is there an average-case virtual gray box obfuscator for evasive Turing machine families.
- Let C be an evasive circuit family consisting of functions that test if a low-degree polynomial (represented by an efficient arithmetic circuit) evaluates to zero modulo some large prime p. Then under a natural analog of the discrete logarithm assumption in a group supporting multilinear maps, there exists an input-hiding obfuscator O for C. Under a new perfectly-hiding multilinear encoding assumption, there is an average-case virtual black box obfuscator for the family C.
Category / Keywords: Date: received 18 Oct 2013 Contact author: omerpa at gmail com Available format(s): PDF | BibTeX Citation Version: 20131024:081651 (All versions of this report) Short URL: ia.cr/2013/668 Discussion forum: Show discussion | Start new discussion