Skyscraper: Fast Hashing on Big Primes

Clémence Bouvier; Lorenzo Grassi; Dmitry Khovratovich; Katharina Koschatko; Christian Rechberger; Fabian Schmid; Markus Schofnegger

Paper 2025/058

Skyscraper: Fast Hashing on Big Primes

Clémence Bouvier

, Université de Lorraine, CNRS, Inria, LORIA, Nancy, France

Lorenzo Grassi

, Ruhr University Bochum, Bochum, Germany, Ponos Technology, Zug, Switzerland

Dmitry Khovratovich

, Ethereum Foundation, Luxembourg, Luxembourg, ABDK Consulting, Tallinn, Estonia

Katharina Koschatko

, Graz University of Technology, Graz, Austria

Christian Rechberger

, Graz University of Technology, Graz, Austria

Fabian Schmid

, Graz University of Technology, Graz, Austria

Markus Schofnegger

, Fabric Cryptography, San Francisco, United States

Abstract

Arithmetic hash functions defined over prime fields have been actively developed and used in verifiable computation (VC) protocols. Among those, elliptic-curve-based SNARKs require large ($256$-bit and higher) primes. Such hash functions are notably slow, losing a factor of up to $1000$ compared to regular constructions like SHA-2/3. In this paper, we present the hash function $\textsf{Skyscraper}$, which is aimed at large prime fields and provides major improvements compared to $\texttt{Reinforced Concrete}$ and $\texttt{Monolith}$. First, the design is exactly the same for all large primes, which simplifies analysis and deployment. Secondly, it achieves a performance comparable to cryptographic hash standards by using low-degree non-invertible transformations and minimizing modulo reductions. Concretely, it hashes two $256$-bit prime field (BLS12-381 curve scalar field) elements in $135$ nanoseconds, whereas SHA-256 needs $42$ nanoseconds on the same machine. The low circuit complexity of $\textsf{Skyscraper}$, together with its high native speed, should allow a substantial reduction in many VC scenarios, particularly in recursive proofs.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Published by the IACR in TCHES 2025
Keywords: Hash functions Zero-knowledge Circuits
Contact author(s): clemence bouvier @ inria fr
lorenzo @ ponos technology
khovratovich @ gmail com
katharina koschatko @ tugraz at
christian rechberger @ tugraz at
fabian schmid @ tugraz at
markus schofnegger @ gmail com
History: 2025-01-16: approved; 2025-01-14: received; See all versions
Short URL: https://ia.cr/2025/058
License: CC BY

BibTeX

@misc{cryptoeprint:2025/058,
      author = {Clémence Bouvier and Lorenzo Grassi and Dmitry Khovratovich and Katharina Koschatko and Christian Rechberger and Fabian Schmid and Markus Schofnegger},
      title = {Skyscraper: Fast Hashing on Big Primes},
      howpublished = {Cryptology {ePrint} Archive, Paper 2025/058},
      year = {2025},
      url = {https://eprint.iacr.org/2025/058}
}