Cryptology ePrint Archive: Report 2020/474

Tiramisu: Black-Box Simulation Extractable NIZKs in the Updatable CRS Model

Karim Baghery and Mahdi Sedaghat

Abstract: In CRYPTO'18, Groth et al. introduced the $\textit{updatable}$ CRS model that allows bypassing the trust in the setup of NIZK arguments. Zk-SNARKs are the well-known family of NIZK arguments that are ubiquitously deployed in practice. In applications that achieve $\textit{universal composability}$, e.g. Hawk [S&P'16], Gyges [CCS'16], Ouroboros Crypsinous [S&P'19], the underlying SNARK is lifted by the $\texttt{COCO}$ framework [Kosba et al.,2015] to achieve Black-Box Simulation Extractability (BB-SE). The $\texttt{COCO}$ framework is designed in the standard CRS model, consequently, the BB-SE NIZK arguments built with it need a trusted setup phase. In a promising research direction, recently subversion-resistant and updatable SNARKs are proposed that can eliminate/bypass the needed trust in schemes. However, none of the available subversion-resistant/updatable schemes can achieve BB-SE, as Bellare et al.'s result from ASIACRYPT'16 shows that achieving simultaneously Sub-ZK (ZK without trusting a third party) and BB extractability is impossible.

In this paper, we propose $\texttt{Tiramisu}$, as construction to build BB-SE NIZK arguments in the $\textit{updatable}$ CRS model. Similar to the $\texttt{COCO}$, $\texttt{Tiramisu}$ is suitable for modular use in larger cryptographic systems and allows building BB-SE NIZK arguments, but with $\textit{updatable}$ parameters. In the cost of one time CRS update, $\texttt{Tiramisu}$ gets arround the mentioned impossibility result by Bellare et al. Namely, by one time updating the CRS, all the parties eliminate the trust on a third-party and the protocol satisfies ZK and BB-SE in the $\textit{updatable}$ CRS model. Meanwhile, we define a variation of public-key cryptosystems with updatable keys, suitable for the updatable CRS model, and present an efficient construction based on the El-Gamal cryptosystem which can be of independent interest. We instantiate $\texttt{Tiramisu}$ and present efficient BB-SE zk-SNARKs with updatable parameters that can be used in protocols like Hawk, Gyges, Ouroboros Crypsinous while allowing the end-users to update the parameters and eliminate the needed trust.

Category / Keywords: cryptographic protocols / zk-SNARKs, Updatable CRS, Black-Box Simulation Extractability, COCO framework, UC-Security

Date: received 22 Apr 2020, last revised 21 Oct 2020

Contact author: baghery karim at gmail com, ssedagha@esat kuleuven be

Available format(s): PDF | BibTeX Citation

Note: In Italian, Tiramisu literally means "pull me up, lift me up", or more literally "pull it up".

Version: 20201021:122634 (All versions of this report)

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