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Succinct non-interactive arguments (SNARGs) enable verifying NP statements with lower complexity than required for classical NP verification. Traditionally, the focus has been on minimizing the length of such arguments; nowadays researches have focused also on minimizing verification time, by drawing motivation from the problem of delegating computation. A(More)
We prove that finding a Nash equilibrium of a game is hard, assuming the existence of indistinguishability obfuscation and one-way functions with sub-exponential hardness. We do so by showing how these cryptographic primitives give rise to a hard computational problem that lies in the complexity class PPAD, for which finding Nash equilibrium is complete.(More)
We study the problem of verifiable delegation of computation over outsourced data, whereby a powerful worker maintains a large data structure for a weak client in a verifiable way. Compared to the well-studied problem of verifiable computation, this setting imposes additional difficulties since the ver-ifier needs to verify consistency of updates succinctly(More)
We construct publicly verifiable non-interactive arguments that can be used to delegate polynomial time computations. These computationally sound proof systems are completely non-interactive in the common reference string model. The verifier's running time is nearly-linear in the input length, and poly-logarithmic in the complexity of the delegated(More)
The goal of general-purpose program obfuscation is to make an arbitrary computer program " unin-telligible " while preserving its functionality. At least as far back as the work of Diffie and Hellman in 1976, researchers have contemplated applications of general-purpose obfuscation. However, until 2013, even heuristic constructions for general-purpose(More)
This work attempts to clarify to what extent simulation-based security (SIM-security) is achievable for functional encryption (FE) and its relation to the weaker indistinguishability-based security (IND-security). Our main result is a compiler that transforms any FE scheme for the general circuit functionality (which we denote by Circuit-FE) meeting(More)
A function <i>f</i> is extractable if it is possible to algorithmically "extract," from any adversarial program that outputs a value <i>y</i> in the image of <i>f;</i> a preimage of <i>y</i>. When combined with hardness properties such as one-wayness or collision-resistance, extractability has proven to be a powerful tool. However, so far, extractability(More)
An evasive circuit family is a collection of circuits C such that for every input x, a random circuit from C outputs 0 on x with overwhelming probability. We provide a combination of definitional, constructive, and impossibility results regarding obfuscation for evasive functions: 1. The (average case variants of the) notions of virtual black box(More)
An obfuscator $$\mathcal {O}$$ O is Virtual Grey Box (VGB) for a class $$\mathcal {C}$$ C of circuits if, for any $$C\in \mathcal {C}$$ C ∈ C and any predicate $$\pi $$ π , deducing $$\pi (C)$$ π ( C ) given $$\mathcal {O}(C)$$ O ( C ) is tantamount to deducing $$\pi (C)$$ π ( C ) given unbounded computational resources and polynomially many oracle queries(More)
The traditional notion of <i>program obfuscation</i> requires that an obfuscation ~Prog of a program Prog computes the exact same function as Prog, but beyond that, the code of ~Prog should not leak any information about Prog. This strong notion of <i>virtual black-box</i> security was shown by Barak et al. (CRYPTO 2001) to be impossible to achieve, for(More)