Appenzeller to Brie: Efficient Zero-Knowledge Proofs for Mixed-Mode Arithmetic and Z2k

Abstract

Zero-knowledge proofs are highly flexible cryptographic protocols that are an important building block for many secure systems. Typically, these are defined with respect to statements that are formulated as arithmetic operations over a fixed finite field. This inflexibility is a disadvantage when it comes to complex programs, as some fields are more amenable to express certain operations than others. At the same time, there do not seem to be many proofs with a programming model similar to those found in modern computer architectures that perform arithmetic with 32 or 64 bit integers.