The existence of non-interactive succinct arguments (namely, non-interactive computationally-sound proof systems where the verifier's time complexity is only polylogarithmically related to the complexity of deciding the language) has been an intriguing question for the past two decades. The question has gained renewed importance in light of the recent interest in delegating computation to untrusted workers. Still, other than Micali's CS proofs in the Random Oracle Model, the only existing candidate construction is based on an elaborate assumption that is tailored to the specific proposal [Di Crescenzo and Lipmaa, CiE '08]. We modify and re-analyze that construction:• We formulate a general and relatively mild notion of extractable collision-resistant hash functions (ECRHs), and show that if ECRHs exist then the modified construction is a non-interactive succinct argument (SNARG) for NP. Furthermore, we show that (a) this construction is a proof of knowledge, and (b) it remains secure against adaptively chosen instances. These two properties are arguably essential for using the construction as a delegation of computation scheme.• We show that existence of SNARGs of knowledge (SNARKs) for NP implies existence of ECRHs, as well as extractable variants of some other cryptographic primitives. This provides further evidence ECRHs are necessary for the existence of SNARKs.• Finally, we propose several quite different candidate ECRHs.Similarly to other extractability (or "knowledge") assumptions, the assumption that ECRHs exist does not fit into the standard mold of cryptographic assumptions. Still, ECRH is a natural and basic primitive that may deserve investigation in of itself. Indeed, we demonstrate its power in obtaining a goal that is provably out of reach in more traditional methods [Gentry and Wichs, STOC '10].

Succinct non-interactive arguments of knowledge (SNARKs) enable verifying NP statements with complexity that is essentially independent of that required for classical NP verification. In particular, they provide strong solutions to the problem of verifiably delegating computation.We construct the first fully-succinct publicly-verifiable SNARK. To do that, we first show how to "bootstrap" any SNARK that requires expensive preprocessing to obtain a SNARK that does not, while preserving public verifiability. We then apply this transformation to known SNARKs with preprocessing. Moreover, the SNARK we construct only requires of the prover time and space that are essentially the same as that required for classical NP verification. Our transformation assumes only collision-resistant hashing; curiously, it does not rely on PCPs. We also show an analogous transformation for privately-verifiable SNARKs, assuming fullyhomomorphic encryption.At the heart of our transformations is a technique for recursive composition of SNARKs. This technique uses in an essential way the proof-carrying data (PCD) framework, which extends SNARKs to the setting of distributed networks of provers and verifiers. Concretely, to bootstrap a given SNARK, we recursively compose the SNARK to obtain a "weak" PCD system for shallow distributed computations, and then use the PCD framework to attain stronger notions of SNARKs and PCD systems.

Using the measurement-based quantum computation model, we construct interactive proofs with non-communicating quantum provers and a classical verifier. Our construction gives interactive proofs for all languages in BQP with a polynomial number of quantum provers, each of which, in the honest case, performs only a single measurement. Our techniques use self-tested graph states. In this regard we introduce two important improvements over previous work. Specifically, we derive new error bounds which scale polynomially with the size of the graph compared with exponential dependence on the size of the graph in previous work. We also extend the self-testing error bounds on measurements to a very general set which includes the adaptive measurements used for measurement-based quantum computation as a special case.

Abstract. The Virtual Black Box (VBB) property for program obfuscators provides a strong guarantee: Anything computable by an efficient adversary given the obfuscated program can also be computed by an efficient simulator with only oracle access to the program. However, we know how to achieve this notion only for very restricted classes of programs.This work studies a simple relaxation of VBB: Allow the simulator unbounded computation time, while still allowing only polynomially many queries to the oracle. We then demonstrate the viability of this relaxed notion, which we call Virtual Grey Box (VGB), in the context of fully composable obfuscators for point programs: It is known that, w.r.t. VBB, if such obfuscators exist then there exist multi-bit point obfuscators (aka "digital lockers") and subsequently also very strong variants of encryption that are resilient to various attacks, such as key leakage and keydependent-messages. However, no composable VBB-obfuscators for point programs have been shown. We show fully composable VGB-obfuscators for point programs under a strong variant of the Decision Diffie Hellman assumption. We show they suffice for the above applications and even for extensions to the public key setting as well as for encryption schemes with resistance to certain related key attacks (RKA).

We put forth a framework for expressing security requirements from interactive protocols in the presence of arbitrary leakage. This allows capturing different levels of leakage tolerance of protocols, namely the preservation (or degradation) of security, under coordinated attacks that include various forms of leakage from the secret states of participating components. The framework extends the universally composable (UC) security framework. We also prove a variant of the UC theorem, that enables modular design and analysis of protocols even in face of general, non-modular leakage.We then construct leakage tolerant protocols for basic tasks, such as, secure message transmission, message authentication, commitment, oblivious transfer and zero knowledge. A central component in several of our constructions is the observation that resilience to adaptive party corruptions (in some strong sense) implies leakage-tolerance in an essentially optimal way.

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.Previous proposals for basing PPAD-hardness on program obfuscation considered a strong "virtual black-box" notion that is subject to severe limitations and is unlikely to be realizable for the programs in question. In contrast, for indistinguishability obfuscation no such limitations are known, and recently, several candidate constructions of indistinguishability obfuscation were suggested based on different hardness assumptions on multilinear maps.Our result provides further evidence of the intractability of finding a Nash equilibrium, one that is extrinsic to the evidence presented so far. * MIT.

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Abstract. A function f is extractable if it is possible to algorithmically "extract," from any adversarial program that outputs a value y in the image of f , a preimage of y. When combined with hardness properties such as one-wayness or collision-resistance, extractability has proven to be a powerful tool. However, so far, extractability has not been explicitly shown. Instead, it has only been considered as a nonstandard knowledge assumption on certain functions. We make headway in the study of the existence of extractable one-way functions (EOWFs) along two directions. On the negative side, we show that if there exist indistinguishability obfuscators for circuits, then there do not exist EOWFs where extraction works for any adversarial program with auxiliary input of unbounded polynomial length. On the positive side, for adversarial programs with bounded auxiliary input (and unbounded polynomial running time), we give the first construction of EOWFs with an explicit extraction procedure, based on relatively standard assumptions (such as subexponential hardness of learning with errors). We then use these functions to construct the first 2-message zero-knowledge arguments and 3-message zero-knowledge arguments of knowledge, against verifiers in the same class of adversarial programs, from essentially the same assumptions.