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**2015/377**

**Title:**

Cluster Computing in Zero Knowledge

**Authors:**
Alessandro Chiesa, Eran Tromer, Madars Virza

**Abstract:**

Large computations, when amenable to distributed parallel execution, are often executed on computer clusters, for scalability and cost reasons. Such computations are used in many applications, including, to name but a few, machine learning, webgraph mining, and statistical machine translation. Oftentimes, though, the input data is private and only the result of the computation can be published. Zero-knowledge proofs would allow, in such settings, to verify correctness of the output without leaking (additional) information about the input. In this work, we investigate theoretical and practical aspects of *zero-knowledge proofs for cluster computations*. We design, build, and evaluate zero-knowledge proof systems for which: (i) a proof attests to the correct execution of a cluster computation; and (ii) generating the proof is itself a cluster computation that is similar in structure and complexity to the original one. Concretely, we focus on MapReduce, an elegant and popular form of cluster computing. Previous zero-knowledge proof systems can in principle prove a MapReduce computationâ€™s correctness, via a monolithic NP statement that reasons about all mappers, all reducers, and shuffling. However, it is not clear how to generate the proof for such monolithic statements via parallel execution by a distributed system. Our work demonstrates, by theory and implementation, that proof generation can be similar in structure and complexity to the original cluster computation. Our main technique is a bootstrapping theorem for succinct non-interactive arguments of knowledge (SNARKs) that shows how, via recursive proof composition and Proof-Carrying Data, it is possible to transform any SNARK into a *distributed SNARK for MapReduce* which proves, piecewise and in a distributed way, the correctness of every step in the original MapReduce computation as well as their global consistency.

**ePrint:**
https://eprint.iacr.org/2015/377

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