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Beyond the Circuit: How to Minimize Foreign Arithmetic in ZKP Circuits (Orrù, Kadianakis, Maller, Zaverucha 2025)

Last modified: 2026-10-27
URL: https://eprint.iacr.org/2024/265

Summary

Gives techniques for embedding "foreign" arithmetic (operations modulo a different prime than the constraint system's field, such as Boolean operations, non-native fields or public-key operations) in zero-knowledge efficiently. It covers equality of discrete logs across groups, scalar multiplication without in-circuit elliptic-curve operations, and proofs of AES encryption, combining rejection sampling, Sigma protocols and lookups. Directly relevant to ECDSA-P256 holder binding, where non-native curve arithmetic dominates circuit cost. Published in IACR Communications in Cryptology 2025.