In this work, we present solutions to both of these problems. First, we show how to efficiently check consistency of secret values between different instances of Zero Knowledge protocols based on the commit-and-prove paradigm. This allows a protocol user to easily switch to the most efficient representation for a given task. To achieve this, we modify the extended doubly-authenticated bits (edabits) approach by Escudero et al. (Crypto 2020), originally developed for MPC, and optimize it for the Zero-Knowledge setting. As an application of our consistency check, we also introduce protocols for efficiently verifying truncations and comparisons of shared values both modulo a large prime $p$ and modulo $2^k$.
Finally, we complement our conversion protocols with new protocols for verifying arithmetic statements in $\mathbb{Z}_{2^k}$. Here, we build upon recent interactive proof systems based on information-theoretic MACs and vector oblivious linear evaluation (VOLE), and show how this paradigm can be adapted to the ring setting. In particular, we show that supporting such modular operations natively in a proof system can be almost as efficient as proofs over large fields or bits, and this also easily plugs into our framework for Zero Knowledge conversions.
Category / Keywords: cryptographic protocols / zero knowledge, commit and prove, rings, conversions Date: received 4 Jun 2021, last revised 15 Jun 2021 Contact author: cbaum at cs au dk, braun at cs au dk, almun at cs au dk, peter scholl at cs au dk Available format(s): PDF | BibTeX Citation Version: 20210615:205135 (All versions of this report) Short URL: ia.cr/2021/750