AffiNiTy: A Multi-Scalar Multiplication Accelerator with a Novel Batched Inversion Architecture

Abstract

Elliptic curve-based zero-knowledge proof (ZKP) protocols typically use multi-scalar multiplication (MSM) as a key primitive, making it one of the major performance bottlenecks in real-world ZK provers. In this paper, we present an FPGA-based MSM accelerator that achieved state-of-the-art performance in the 2023 ZPrize, a competition dedicated to advancing zero-knowledge cryptography, with submissions from both academia and industry. Our design achieves this through two primary innovations. First, we adopt affine (two-coordinate) representations for elliptic curve points, rather than resorting to projective coordinates, and leverage a batched inversion strategy to handle the expensive multiplicative inverse operation. Although many implementations extend points to projective form to avoid explicit inversions, they incur additional multiplications. By retaining affine coordinates and using the Montgomery trick (where multiple denominators are inverted at once), our accelerator reduces the overall number of real inversions per batch of point additions, drastically improving throughput while preserving a simpler coordinate system. Second, we introduce a novel hazard avoidance scheme that eliminates pipeline stalls arising from our high-latency elliptic curve addition pipeline. Through early detection and reordering of hazards, the pipeline remains fully utilized, thus maintaining continuous high throughput.