Cryptology ePrint Archive: Report 2020/1212

Triply Adaptive UC NIZK

Ran Canetti and Pratik Sarkar and Xiao Wang

Abstract: The only known non-interactive zero-knowledge (NIZK) protocol that is secure against adaptive corruption of the prover is based on that of Groth-Ostrovsky-Sahai (JACM'11) (GOS). However that protocol does not guarantee full adaptive soundness. Abe and Fehr (TCC'07) construct an adaptively sound variant of the GOS protocol under a knowledge-of-exponent assumption, but knowledge assumptions of this type are inherently incompatible with universally composable (UC) security.

We show the first NIZK which is triply adaptive: it is a UC NIZK protocol in a multi-party, multi-instance setting, with adaptive corruptions and no data erasures. Furthermore, the protocol provides full adaptive soundness. Our construction is very different than that of GOS: it is based on the recent NIZK of Canetti et al (STOC'19), and can be based on a variety of assumptions (e.g. LWE, or LPN and DDH). We also show how to get a succinct reference string assuming LWE or DDH from GOS-like techniques.

Category / Keywords: cryptographic protocols / Non-interactive Zero Knowledge, Correlation Intractability, Adaptive Security

Date: received 2 Oct 2020, last revised 7 Oct 2020

Contact author: canetti at bu edu,pratik93@bu edu,wangxiao@cs northwestern edu

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Version: 20201007:070252 (All versions of this report)

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