Paper 2026/1931

SoK: Zero-Knowledge Friendly Hash Functions over Prime Fields

Abstract

Zero-Knowledge (ZK) proof systems have become a cornerstone of privacy-preserving technologies and blockchain scalability. However, traditional hash functions are often inefficient within ZK protocols due to their high constraint complexity in arithmetic circuits. While various ZK-friendly hash functions have been proposed to address this bottleneck, their diverse algebraic structures and varying security margins make it difficult for practitioners to select the optimal primitive. We conduct a systematic survey of ZK-friendly hash functions, covering both algorithmic design paradigms and modes of operation. We consolidate the relevant algebraic cryptanalysis techniques and review the third-party cryptanalysis of each design. For parameter sets broken by the best known attacks, we estimate the minimum number of rounds needed to withstand them - not as new recommendations, but to bring all constructions to a comparable level. On this basis, we analyze each construction across different arithmetization styles (R1CS, AIR, PLONK), both theoretically, by deriving the underlying constraint or gate counts, and empirically, through extensive benchmarks. This paper comes with a fully open-source implementation suite comprising a SageMath/Python reference framework, native Rust implementations, in-circuit implementations, and a reusable TikZ figure library.