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Published at ASIACRYPT 2025
Hashing-to-Curve is a fundamental operation in many cryptographic applications, including multiset hashing and BLS signatures. With the rapid development of zero-knowledge proof applications, this operation is increasingly being used in constraint programming environments. For example, multiset hashing is employed for memory consistency checks in zkVMs, while BLS signatures are widely utilized in Proof-of-Stake (PoS) protocols. In these applications, the construction of Hashing-to-Curve must be constraint-friendly to efficiently generate concise proofs of correctness. However, existing constructions typically rely on cryptographic hash functions, which are expensive to represent in arithmetic constraint systems, leading to high proving costs.
To address this, we propose a constraint-efficient alternative: a mapping relation to elliptic curve groups that eliminates the need for cryptographic hash functions. This mapping can directly replace existing hashing-to-curve constructions in the aforementioned practical scenarios. It natively supports non-deterministic mapping, making it more efficient in constraint programming frameworks and enabling effective integration into zero-knowledge proofs. We formalize the security of this approach under the Elliptic Curve Generic Group Model (EC-GGM).
Our implementation in Noir/Barretenberg demonstrates the efficiency of this construction in constraint programming: compared to state-of-the-art hashing-to-curve methods, our approach significantly reduces the number of constraints and markedly accelerates proving times in large-scale scenarios.
Published at ASIACRYPT 2025
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