Cryptology ePrint Archive: Report 2014/981

Publicly Verifiable Non-Interactive Arguments for Delegating Computation

Omer Paneth and Guy N. Rothblum

Abstract: 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 computation. Our protocol is based on graded encoding schemes, introduced by Garg, Gentry and Halevi (Eurocrypt 2012). Security is proved under a falsifiable and arguably simple cryptographic assumption about graded encodings. All prior publicly verifiable non-interactive argument systems were based on non-falsifiable knowledge assumptions. Our new result builds on the beautiful recent work of Kalai, Raz and Rothblum (STOC 2014), who constructed privately verifiable 2-message arguments. While building on their techniques, our protocols avoid no-signaling PCPs, and we obtain a simplified and modular analysis.

As a second contribution, we also construct a publicly verifiable non-interactive argument for (logspace-uniform) computations of bounded depth. The verifier's complexity grows with the depth of the circuit. This second protocol is adaptively sound, and its security is based on a falsifiable assumption about the hardness of a search problem on graded encodings (a milder cryptographic assumption). This result builds on the interactive proof of Goldwasser, Kalai and Rothblum (STOC 2008), using graded encodings to construct a non-interactive version of their protocol.

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Date: received 4 Dec 2014

Contact author: omerpa at gmail com

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Version: 20141207:153241 (All versions of this report)

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