Succinct Arguments over Towers of Binary Fields

We introduce an efficient SNARK for towers of binary fields. Adapting Brakedown (CRYPTO '23), we construct a multilinear polynomial commitment scheme suitable for polynomials over tiny fields, including that with just two elements. Our commitment scheme, unlike those of previous works, treats small-field polynomials with no embedding overhead. We further introduce binary-field adaptations of HyperPlonk (EUROCRYPT '23)'s product and permutation checks and of Lasso (EUROCRYPT '24)'s lookup. Our binary PLONKish variant captures standard hash functions—like Keccak-256 and Grøstl—extremely efficiently. With recourse to thorough performance benchmarks, we argue that our scheme can efficiently generate precisely those Keccak-256-proofs which critically underlie modern efforts to scale Ethereum.