IACR News item: 16 January 2025
Clémence Bouvier, Lorenzo Grassi, Dmitry Khovratovich, Katharina Koschatko, Christian Rechberger, Fabian Schmid, Markus Schofnegger
ePrint Report
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.
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.
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