Succinct Non-interactive Arguments via Linear Interactive Proofs

Abstract

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.

Verifiable Computation in Multiparty Protocols with Honest Majority

“…In [22], Yao's garbled circuits [36] are executed using fully homomorphic encryption. Quadratic span programs for boolean circuits and quadratic arithmetic programs for arithmetic circuits without PCP have first been proposed in [23], later extended to PCP by [6], and further optimized and improved in [5,28,31]. Particular implementations of verifiable computations have been done for example in [5,31,34].…”

“…Similarly to different approaches to verifiable computation [5,6,23,28,31], in our work we let the relation R to correspond to the circuit C executed by the party whose observance of the protocol is being verified. In this correspondence, v is the tuple of all inputs, outputs, and used random values of that party.…”

“…This linear interactive proof can be converted to a zero-knowledge succinct non-interactive argument of knowledge [6]. Unfortunately, it requires homomorphic encryption, and the number of encryptions is linear in the size of the circuit.…”

Efficient Non-Interactive Zero Knowledge Arguments for Set Operations

“…3 Here and in what follows, elements of the form (g, g α ) x , where α is a secret random key, can be thought of as a linear-only encoding of x, see [5] for a discussion…”

“…For the rest of this introduction, we recall that sublinear NIZK proofs can only be (a) computationally sound, and (b) cannot be based on standard (falsifiable) assumptions [25]. Thus, following a long line of contemporary cryptographic research [28,14,36,24,5,3,21,37], we will construct NIZK arguments that are sound under some knowledge assumptions.…”