Welcome to the resource topic for 2022/819
Title:
Moz$\mathbb{Z}{2^k}arella: Efficient Vector-OLE and Zero-Knowledge Proofs Over \mathbb{Z}{2^k}$
Authors: Carsten Baum, Lennart Braun, Alexander Munch-Hansen, and Peter Scholl
Abstract:Zero-knowledge proof systems are usually designed to support computations for circuits over \mathbb{F}_2 or \mathbb{F}_p for large p, but not for computations over \mathbb{Z}_{2^k}, which all modern CPUs operate on. Although \mathbb{Z}_{2^k}-arithmetic can be emulated using prime moduli, this comes with an unavoidable overhead. Recently, Baum et al. (CCS 2021) suggested a candidate construction for a designated-verifier zero-knowledge proof system that natively runs over \mathbb{Z}_{2^k}. Unfortunately, their construction requires preprocessed random vector oblivious linear evaluation (VOLE) to be instantiated over \mathbb{Z}_{2^k}. Currently, it is not known how to efficiently generate such random VOLE in large quantities. In this work, we present a maliciously secure, VOLE extension protocol that can turn a short seed-VOLE over \mathbb{Z}_{2^k} into a much longer, pseudorandom VOLE over the same ring. Our construction borrows ideas from recent protocols over finite fields, which we non-trivially adapt to work over \mathbb{Z}_{2^k}. Moreover, we show that the approach taken by the QuickSilver zero-knowledge proof system (Yang et al. CCS 2021) can be generalized to support computations over \mathbb{Z}_{2^k}. This new VOLE-based proof system, which we call QuarkSilver, yields better efficiency than the previous zero-knowledge protocols suggested by Baum et al. Furthermore, we implement both our VOLE extension and our zero-knowledge proof system, and show that they can generate 13-50 million VOLEs per second for 64 to 256 bit rings, and evaluate 1.3 million 64 bit multiplications per second in zero-knowledge.
ePrint: https://eprint.iacr.org/2022/819
Talk: https://www.youtube.com/watch?v=3loWvN8uiSA
Slides: https://iacr.org/submit/files/slides/2022/crypto/crypto2022/404/slides.pdf
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