BN254 CUDA

• GPU-accelerated field arithmetic operations
• Montgomery multiplication optimization
• Batch processing (thousands of elements in parallel)
• 20-60x speedup over CPU implementations
• Comprehensive test suites
• Educational implementation with detailed comments

Overview

BN254 CUDA implements finite field arithmetic operations for the BN254 elliptic curve using CUDA acceleration. The project demonstrates GPU optimization techniques for cryptographic computations, serving as a foundation for Zero Knowledge Proof system acceleration.

Tech Stack

• CUDA Toolkit 11.0+
• NVIDIA GPU (Compute capability 7.0+)
• CMake 3.18+ build system
• C++/CUDA C++

Performance

Benchmarked on NVIDIA RTX 4080:

Key Features

Field Arithmetic: GPU-accelerated modular addition, subtraction, and multiplication with automatic reduction and overflow handling for BN254 finite field operations.

Montgomery Multiplication: Optimized Montgomery form arithmetic enabling efficient batch processing of cryptographic operations without expensive modular reductions.

Batch Processing: Parallel computation across thousands of field elements simultaneously, maximizing GPU utilization for high-throughput cryptographic workloads.

Educational Design: Progressive complexity with detailed algorithm comments, debug modes, and CPU reference implementations for learning GPU optimization techniques.

Architecture

// Example: Batch Montgomery multiplication on GPU
__global__ void montgomery_mult_kernel(
    const FieldElement* a,
    const FieldElement* b,
    FieldElement* result,
    size_t n
) {
    int idx = blockIdx.x * blockDim.x + threadIdx.x;
    if (idx < n) {
        result[idx] = montgomery_mult(a[idx], b[idx]);
    }
}

BN254 Parameters

• Prime modulus: 21888242871839275222246405745257275088696311157297823662689037894645226208583
• Precision: 256-bit (4 × 64-bit limbs)
• Curve equation: y² = x³ + 3
• Montgomery constants: Optimized for GPU architectures

Applications

Foundation for GPU-accelerated Zero Knowledge Proof systems including Nova folding, PLONK/Groth16 proof generation, and elliptic curve cryptography research. An earlier development line of the same Pippenger superstructure that the Pallas MSM kernels in my thesis were built on.