1970-01-01

(2026-02) PANCAKE; A SNARK with Plonkish Constraints, Almost-Free Additions, No Permutation Check, and a Linear-Time Prover

• [[Yuxi Xue]]
• [[Peimin Gao]]
• [[Xingye Lu]]
• [[Man Ho Au]]

2026-02-10

• #cryptography
• #paper

Abstract

This paper presents (\mathsf{Pancake}), a linear-time SNARK with a circuit-specific setup that eliminates the explicit representation and separate verification of addition gates in Plonkish constraint systems. Specifically, we consolidate wiring constraints and addition-gate constraints into a single family of general linear constraints, which can be enforced efficiently via a single sumcheck protocol. As a result, (\mathsf{Pancake}) achieves ``almost-free'' addition gates, which significantly reduces the witness size and directly improves prover efficiency while preserving full support for high-degree custom gates.

Our implementation shows that (\mathsf{Pancake}) outperforms the state-of-the-art Plonkish SNARK (\mathsf{HyperPlonk}) (Chen et al., EUROCRYPT 2023) in terms of prover efficiency. For a circuit size of $2^{24}$ where half the gates are additions, (\mathsf{Pancake}) achieves prover speedups of $1.67\times$ (single-threaded) and $2.43\times$ (32-threaded), while also generating smaller proofs and maintaining comparable verification time.