International Association
for Cryptologic Research

Zero-knowledge Succinct Non-interactive ARguments of Knowledge (zkSNARKs) are becoming an increasingly fundamental tool in many real-world applications where the proof compactness is of the utmost importance, including blockchains. A proof of security for SNARKs in the Universal Composability (UC) framework (Canetti, FOCS'01) would rule out devastating malleability attacks. To retain security of SNARKs in the UC model, one must show their \emph{simulation-extractability} such that the knowledge extractor is both \emph{black-box} and \emph{straight-line}, which would imply that proofs generated by honest provers are \emph{non-malleable}. However, existing simulation-extractability results on SNARKs either lack some of these properties, or alternatively have to sacrifice \emph{witness succinctness} to prove UC security. In this paper, we provide a compiler lifting any simulation-extractable NIZKAoK into a UC-secure one in the global random oracle model, importantly, while preserving the same level of witness succinctness. Combining this with existing zkSNARKs, we achieve, to the best of our knowledge, the first zkSNARKs simultaneously achieving UC-security and constant sized proofs.

Most succinct arguments (SNARKs) are initially only proven knowledge sound (KS). We show that the commonly employed compilation strategy from polynomial interactive oracle proofs (PIOP) via polynomial commitments to knowledge sound SNARKS actually also achieves other desirable properties: weak unique response (WUR) and trapdoorless zero-knowledge (TLZK); and that together they imply simulation extractability (SIM-EXT). The factoring of SIM-EXT into KS + WUR + TLZK is becoming a cornerstone of the analysis of non-malleable SNARK systems. We show how to prove WUR (and TLZK) for PIOP compiled SNARKs under mild falsifiable assumptions on the polynomial commitment scheme. This means that the analysis of knowledge soundness from PIOP properties that inherently relies on non-falsifiable or idealized assumption such as the algebraic group model (AGM) or generic group model (GGM) need not be repeated. While the proof of WUR requires only mild assumptions on the PIOP, TLZK is a different matter. As perfectly hiding polynomial commitments sometimes come at a substantial performance premium, SNARK designers prefer to employ deterministic commitments with some leakage. This results in the need for a stronger zero-knowledge property for the PIOP. The modularity of our approach implies that any analysis improvements, e.g. in terms of tightness, credibility of the knowledge assumption and model of the KS analysis, or the precision of capturing real-world optimizations for TLZK also benefits the SIM-EXT guarantees.

Bulletproofs (B{\"u}nz et al.~IEEE S\&P 2018) are a celebrated ZK proof system that allows for short and efficient proofs, and have been implemented and deployed in several real-world systems. In practice, they are most often implemented in their \emph{non-interactive} version obtained using the Fiat-Shamir transform, despite the lack of a formal proof of security for this setting. Prior to this work, there was no evidence that \emph{malleability attacks} were not possible against Fiat-Shamir Bulletproofs. Malleability attacks can lead to very severe vulnerabilities, as they allow an adversary to forge proofs re-using or modifying parts of the proofs provided by the honest parties. In this paper, we show for the first time that Bulletproofs (or any other similar multi-round proof system satisfying some form of \emph{weak unique response} property) achieve \emph{simulation-extractability} in the \emph{algebraic group model}. This implies that Fiat-Shamir Bulletproofs are \emph{non-malleable}.

We study Multi-party computation (MPC) in the setting of subversion, where the adversary tampers with the machines of honest parties. Our goal is to construct actively secure MPC protocols where parties are corrupted adaptively by an adversary (as in the standard adaptive security setting), and in addition, honest parties' machines are compromised. The idea of reverse firewalls (RF) was introduced at EUROCRYPT'15 by Mironov and Stephens-Davidowitz as an approach to protecting protocols against corruption of honest parties' devices. Intuitively, an RF for a party $\mathcal{P}$ is an external entity that sits between $\mathcal{P}$ and the outside world and whose scope is to sanitize $\mathcal{P}$’s incoming and outgoing messages in the face of subversion of their computer. Mironov and Stephens-Davidowitz constructed a protocol for passively-secure two-party computation. At CRYPTO'20, Chakraborty, Dziembowski and Nielsen constructed a protocol for secure computation with firewalls that improved on this result, both by extending it to \textit{multi}-party computation protocol, and considering \textit{active} security in the presence of \textit{static} corruptions. In this paper, we initiate the study of RF for MPC in the \textit{adaptive} setting. We put forward a definition for adaptively secure MPC in the reverse firewall setting, explore relationships among the security notions, and then construct reverse firewalls for MPC in this stronger setting of adaptive security. We also resolve the open question of Chakraborty, Dziembowski and Nielsen by removing the need for a trusted setup in constructing RF for MPC. Towards this end, we construct reverse firewalls for adaptively secure augmented coin tossing and adaptively secure zero-knowledge protocols and obtain a constant round adaptively secure MPC protocol in the reverse firewall setting without setup. Along the way, we propose a new multi-party adaptively secure coin tossing protocol in the plain model, that is of independent interest.