RainHash2.0: Hardware- and Arithmetization-friendly Hash Function

Jiamin Cui; Lorenzo Grassi; Katharina Koschatko; Florian Krieger; Shibam Mukherjee; Christian Rechberger; Sujoy Sinha Roy; Markus Schofnegger; Verena Schröppel

Paper 2026/1441

RainHash2.0: Hardware- and Arithmetization-friendly Hash Function

Jiamin Cui

, Shandong University, Qingdao, China

Lorenzo Grassi

, Eindhoven University of Technology, Eindhoven, Netherlands, Ponos Technology, Zug, Switzerland

Katharina Koschatko

, Graz University of Technology, Graz, Austria

Florian Krieger

, Graz University of Technology, Graz, Austria

Shibam Mukherjee

, Graz University of Technology, Graz, Austria, Know Center, Graz, Austria

Christian Rechberger

, Graz University of Technology, Graz, Austria, TACEO, Graz, Austria

Sujoy Sinha Roy

, Graz University of Technology, Graz, Austria

Markus Schofnegger

, [[alloc] init], San Francisco, United States

Verena Schröppel

, Graz University of Technology, Graz, Austria, TACEO, Graz, Austria

Abstract

Zero-knowledge (ZK) proof systems have developed rapidly in recent years, with hash functions as one of their central building blocks. Since these often dominate the prover cost, circuit-friendly hash function design has become an active research area. Most hash proposals target prime fields, although recent protocols such as Binius and VOLE-based ZK operate natively over binary extension fields $\mathbb{F}_{2^n}$. These binary field protocols reduce the cost of proving widely used binary and bitwise statements, thereby opening up new design opportunities. At the same time, the demand for ZK applications such as zkRollups is pushing towards performant hardware acceleration, a requirement that recent designs have largely neglected. Hence, a modern ZK hash function should also be efficient in hardware and fast in plain evaluation, to avoid new bottlenecks in non-circuit workloads. In this paper, we introduce RainHash2.0, a cryptographic permutation that addresses both gaps. RainHash2.0 is natively defined over binary extension fields, making it a natural match for $\mathbb{F}_{2^n}$-based protocols such as Binius and VOLEitH, while being tailored for efficient hardware and competitive plain performance. To achieve this, we exploit new techniques from Binius to horizontally split the round function - arguably a novelty in itself that is particularly effective when finite fields of different sizes are used simultaneously. We implement RainHash2.0 in the Binius and VOLE-based ZK frameworks, comparing it against SHAKE, recent arithmetization-oriented designs, and its direct predecessor RainHash. Across proof size, prover- and verifier runtime, RainHash2.0 delivers significant improvements. In addition, we prototype RainHash2.0 on FPGA hardware and reach efficiency gains of up to 8.8$\times$ over related circuit-friendly hash functions. These results mark RainHash2.0 a practical choice for modern ZK applications.

Note: All implementations and experimental results are available at https://extgit.isec.tugraz.at/krypto/rainhash2.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Preprint.
Keywords: Hash Function Zero Knowledge Binius VOLEitH Hardware Acceleration Binary Extension Fields RainHash RainHash2.0
Contact author(s): cuijiamin @ sdu edu cn
l grassi @ tue nl
katharina koschatko @ tugraz at
florian krieger @ tugraz at
shibam mukherjee @ tugraz at
christian rechberger @ tugraz at
sujoy sinharoy @ tugraz at
markus schofnegger @ gmail com
verena schroeppel @ tugraz at
History: 2026-07-16: approved; 2026-07-15: received; See all versions
Short URL: https://ia.cr/2026/1441
License: CC BY

BibTeX

@misc{cryptoeprint:2026/1441,
      author = {Jiamin Cui and Lorenzo Grassi and Katharina Koschatko and Florian Krieger and Shibam Mukherjee and Christian Rechberger and Sujoy Sinha Roy and Markus Schofnegger and Verena Schröppel},
      title = {{RainHash2}.0: Hardware- and Arithmetization-friendly Hash Function},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/1441},
      year = {2026},
      url = {https://eprint.iacr.org/2026/1441}
}