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0.3.0-alpha.1	Apr 27, 2023

#1145 in Cryptography

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MIT/Apache

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ark-msm

ark-msm is a Multi-Scalar Multiplication (MSM) module that incorporates state-of-the-art MSM optimizations into arkworks. This implementation is extensively documented, enabling developers to quickly learn and experiment with lastest MSM optimization techniques. Additionally, the code is designed to be modular, facilitating easy integration with other libraries and projects.

Please note that the current implementation is intended for research and study purposes only and has not been audited for production use. Use at your own discretion.

Up to 2x Performance Speedup

The table below presents a comparison of the latencies of ark-msm and Arkworks 3.0 (baseline) on input sizes ranging from 2^8 to 2^18. Overall, ark-msm achieved up to 2x speedup over the baseline.

Input Size (ms)	2^8	2^9	2^10	2^11	2^12	2^13	2^14	2^15	2^16	2^17	2^18
Arkworks 3.0	13.903	24.208	37.5	67.545	121.03	204.92	375.85	693.46	1268.6	2324.9	4391.9
Arkmsm	7.665	11.982	19.514	33.197	60.593	110.68	204.33	375.17	711.6	1372.1	2742.1
Speedup	1.81	2.02	1.92	2.03	2.00	1.85	1.84	1.85	1.78	1.69	1.60

Performance measured on a AMD EPYC 7282 16-Core Processor.

Optimizations

The following optimization techniques were used on top of the Pippenger Algorithm used in Arkworks.

Batch Addition in Bucket Accumulation (Batch Accumulation)
Batch Addition in Bucket Reduction (Batch Reduction)
Signed Bucket Indexes (Signed Index)
GLV Decomposition (GLV)

Each optimization is implemented in a separate commit so that the impact of each optimization can be accurately measured.

The table below presents a detailed breakdown of the performance improvements achieved with each optimization technique with a 2^12 intput size.

	Latency (ms)	Improvement
Baseline	121.03
Batch Accumulation	92.154	31.33%
Signed Index	74.429	23.81%
Batch Reductio	65.023	14.47%
GLV	60.593	7.31%
Overall		99.74%

Documentation

Detailed documentations about each optimization are available at https://hackmd.io/@drouyang/msm

Getting Started

Install Rust:

curl --proto '=https' --tlsv1.2 -sSf https://sh.rustup.rs | sh
source $HOME/.cargo/env

Run Unittests:
```
cargo test
```

Run Benchmarks:

cargo bench -- bench_with_baseline
cargo bench -- bench_window_size

Acknowledgement

The ark-msm project was funded by a grant from the MINA Foundation.

Our algorithms and implementations were heavily based on the 2022 zPrize submission from Yrrid software written in C.

We would like to acknowledge Gregor Mitscha-Baude from O(1) Labs and Niall Emmart from Yrrid Software for generously taking the time to answer our technical questions.

Questions

For technical questions, please contact ouyang at snarikify.io

Dependencies

~2.4–3.5MB
~64K SLoC