Paper 2026/1698 Original: eprint.iacr.org/2026/1698 ↗

MamaBearZKP: A Holistic Co-design of Prime Fields and Proving Stacks for High-Throughput ZKP on Modern CPUs

Abstract

Sum-check and Fast Fourier Transforms (FFTs) dominate the computational cost of modern zero-knowledge proving systems, such as HyperPlonk (Eurocrypt 2023) and FRI-based schemes like DeepFold (USENIX Security 2025). Despite numerous optimizations, existing efforts remain fragmented across algorithmic, protocol, and implementation layers, leaving significant CPU performance potential untapped. We present MamaBearZKP, a co-designed framework that bridges these layers to enable high-throughput ZK proving on modern CPUs. At its core, MamaBearZKP leverages MamaBear, a 49-bit prime field ($p = 2^{49} - 2^{34} + 1$), and introduces a systematic vectorization framework specifically tailored for the AVX-512IFMA execution model. By treating field arithmetic, protocol structure, and low-level hardware primitives as a unified optimization target, MamaBearZKP achieves unprecedented efficiency. We instantiate our framework in a HyperPlonk-DeepFold prover and obtain single-thread speedups of up to $42\times$, $33\times$, $15\times$, $21\times$, and $21\times$ for ZeroCheck, ProductCheck, DeepFold Commit, DeepFold Open, and end-to-end proof generation, respectively, compared to a Goldilocks-based baseline on the same platform. With 8-thread execution, the corresponding speedups increase to as much as $64\times$, $47\times$, $81\times$, $45\times$, and $45\times$. Across our end-to-end evaluations, MamaBearZKP also achieves up to $18\times$ single-thread speedup over Plonky3, which already uses an AVX-512 BabyBear backend. Rather than resulting from isolated improvements, these gains arise from a synergistic cascading effect: the 49-bit field’s headroom enables efficient lazy reduction, which paves the way for high-performance fused fold-and-evaluate kernels. The efficiency of these kernels facilitates a unified stay-packed dataflow throughout the HyperPlonk and DeepFold stacks; it is precisely this end-to-end dataflow that materializes the hardware throughput of AVX-512IFMA into realized performance gains.