BN254-Fq GPU

• CUDA GPU kernels for field operations and MSM
• Rust wrapper with arkworks compatibility
• Montgomery form arithmetic for efficiency
• Projective coordinate point operations
• Pippenger's bucket method for MSM
• Up to 6.25x speedup over CPU implementation

Overview

BN254-Fq GPU is a high-performance implementation of multi-scalar multiplication (MSM) for the BN254 elliptic curve using CUDA acceleration. The project provides low-level GPU kernels wrapped in a Rust API compatible with the arkworks ecosystem, enabling significant performance improvements for Zero Knowledge Proof systems.

Tech Stack

GPU Acceleration

• CUDA 11.0+ for parallel field operations
• NVIDIA GPU (Compute capability 7.0+)
• Custom kernels for Montgomery arithmetic

High-Level Interface

• Rust 1.70+
• arkworks (ark-bn254) integration
• Dual CPU/GPU implementations

Performance

Benchmarked on NVIDIA RTX 3080 vs AMD Ryzen 9 5900X:

Key Features

Field Operations: GPU-accelerated addition, subtraction, multiplication, squaring, and inversion on the BN254 base field (Fq) using Montgomery representation for efficient modular arithmetic.

Point Arithmetic: Projective coordinate operations including point doubling, addition, and mixed addition optimized for parallel execution on GPU hardware.

Multi-Scalar Multiplication: Parallel MSM implementation using Pippenger's bucket method, the standard algorithm for computing linear combinations of elliptic curve points efficiently.

arkworks Integration: Seamless interoperability with the arkworks cryptography library, providing a familiar API for Rust developers working with Zero Knowledge Proof systems.

BN254 Curve Parameters

• Base Field (Fq): 254-bit prime field
• Scalar Field (Fr): 254-bit prime field
• Curve Equation: y² = x³ + 3
• Representation: 4 × 64-bit limbs (little-endian)

Architecture

// Example: GPU-accelerated MSM
use bn254_fq_gpu::{msm_gpu, G1Affine, Fr};
 
let bases: Vec<G1Affine> = load_points();
let scalars: Vec<Fr> = load_scalars();
 
// Compute MSM on GPU
let result = msm_gpu(&bases, &scalars)?;

The implementation separates concerns between CUDA kernels for low-level field arithmetic and Rust wrappers providing type-safe, ergonomic APIs.

Applications

Critical component for accelerating Zero Knowledge Proof systems including:

• Nova folding framework optimization
• PLONK/Groth16 proof generation
• BN254-based zkSNARK protocols
• Hardware acceleration research for cryptographic workloads

This project directly supports research into FPGA vs GPU performance comparisons for ZKP systems.