Paper Info
Title
Mac'N'Cheese: Zero-Knowledge Proofs For Boolean And Arithmetic Circuits With Nested Disjunctions
Abstract
Zero knowledge proofs are an important building block in many cryptographic applications. Unfortunately, when the proof statements become very large, existing zero-knowledge proof systems easily reach their limits: either the computational overhead, the memory footprint, or the required bandwidth exceed levels that would be tolerable in practice.We present an interactive zero-knowledge proof system for boolean and arithmetic circuits, called Mac ' n ' Cheese , with a focus on supporting large circuits. Our work follows the commit-and-prove paradigm instantiated using information-theoretic MACs based on vector oblivious linear evaluation to achieve high efficiency. We additionally show how to optimize disjunctions, with a general OR transformation for proving the disjunction of m statements that has communication complexity proportional to the longest statement (plus an additive term logarithmic in m). These disjunctions can further be nested, allowing efficient proofs about complex statements with many levels of disjunctions. We also show how to make Mac ' n ' Cheese non-interactive (after a preprocessing phase) using the Fiat-Shamir transform, and with only a small degradation in soundness.We have implemented the online phase of Mac ' n ' Cheese and achieve a runtime of 144 ns per AND gate and 1.5 mu s per multiplication gate in F(2)61(-1) when run over a network with a 95 ms latency and a bandwidth of 31.5 Mbps. In addition, we show that the disjunction optimization improves communication as expected: when proving a boolean circuit with eight branches and each branch containing roughly 1 billion multiplications, Mac'n'Cheese requires only 75 more bytes to communicate than in the single branch case.
Year
DOI
Venue
2021
10.1007/978-3-030-84259-8_4
ADVANCES IN CRYPTOLOGY - CRYPTO 2021, PT IV
DocType
Volume
ISSN
Conference
12828
0302-9743
Citations 
PageRank 
References 
0
0.34
0
Authors
4
Name
Order
Citations
PageRank
Carsten Baum1529.67
Alex J. Malozemoff21588.98
Marc B. Rosen300.34
Peter Scholl401.35