Constraint-Level Design of zkEVMs: Architectures, Trade-offs, and Evolution

Abstract

Zero-Knowledge Ethereum Virtual Machines (zkEVMs) face an inherent tension. The Ethereum Virtual Machine (EVM) was built for transparent step-by-step execution. Proving that execution in zero-knowledge requires recasting it as algebraic circuits that encode computation as mathematical constraints. Existing surveys address zkEVMs at the level of implementations, cryptographic primitives, or Layer 2 deployment, leaving the constraint-system design that governs their cost largely unexamined. This survey provides the first constraint-level analysis of how production zkEVMs and universal Zero-Knowledge Virtual Machines (zkVMs) resolve this tension. We show that the degree of EVM compatibility, captured by the Type 1-4 spectrum, is the defining architectural decision. We classify the design space along four dimensions, namely arithmetization frameworks, dispatch strategies, semantic rewrites, and recursion approaches. The most Ethereum-equivalent systems accept higher constraint counts to preserve full bytecode fidelity, while those that relax fidelity attain lower constraint cost. We close with the open problems that this constraint-level view brings into focus.