This is a GPU Groth16 prover that won the 2x speedup prize. It follows the template from the reference.

This prover requires a substantial amount of RAM to use. The reference machine has 32GB.

This prover has a slow preprocessing step! Note the changed instructions below.

The code should compile and run on Ubuntu 18.04 with the following dependencies installed:

sudo apt-get install -y build-essential \
    cmake \
    git \
    libomp-dev \
    libgmp3-dev \
    libprocps-dev \
    python-markdown \
    libboost-all-dev \
    libssl-dev \
    pkg-config \
    nvidia-cuda-toolkit

Building on MacOS is not recommended as CUDA support is harder to use. (Apple mostly ships with AMD.)

./build.sh

./generate_parameters
./main MNT4753 preprocess MNT4753-parameters # IMPORTANT PREPROCESSING STEPS
./main MNT6753 preprocess MNT6753-parameters

The preprocessed filenames are currently hardcoded to MNT4753_preprocessed and MNT6753_preprocessed.

./main MNT4753 compute MNT4753-parameters MNT4753-input MNT4753-output
./main MNT6753 compute MNT6753-parameters MNT6753-input MNT6753-output
./cuda_prover_piecewise MNT4753 compute MNT4753-parameters MNT4753-input MNT4753-output_cuda
./cuda_prover_piecewise MNT6753 compute MNT6753-parameters MNT6753-input MNT6753-output_cuda

sha256sum MNT4753-output MNT6753-output MNT4753-output_cuda MNT6753-output_cuda

There are 3 components to this SNARK prover which can be optimized.

The multiexponentiations are still the bottleneck and optimization efforts should probably be focused there right now.

• The current best implementation performs a "map-reduce" to implement the multiexponentiation with a batched double-and-add being the base multiexponentiation "map" function. The Pippenger algorithm (described here and implemented for another curve here is likely to be significantly faster.

• The above remarks about the Pippenger algorithm also apply here. To repeat, the current best implementation performs a "map-reduce" to implement the multiexponentiation with a batched double-and-add being the base multiexponentiation "map" function. The Pippenger algorithm (described here and implemented for another curve here is likely to be significantly faster.

• The technique in this paper can be used to speed up the G2 multi-exponentiation by about 2x.

This implementation did not implement the fast-fourier-transform for the GPU and used the existing C++ CPU implementation. It may be possible to get additional speedups by implementing the FFT on the GPU, although the current-best implementation performs the FFT on the CPU while the GPU is busy working, so it may not be blocking anything at the moment.