MSM

Overview

The Multi-Scalar Multiplication (MSM) operation consists of multiplying a vector of finite field elements by a vector of elliptic curve points and summing the resulting vector into a single point. The Pippenger bucketing algorithm is typically applied, and well-documented in existing literature [REF]. The cuSnark library utilizes a generalized version of the winning 2022 zprize MSM implementation, documentation of which can be found here [REF].

Performance

The following table outlines the performance improvements yielded with just the cuSnark MSM employed, showing the (CPU baseline) and accelerated results for the different proof stages in a set of proofs of various sizes. Times are in seconds, obtained on a AMD EPYC 7702 64-Core Processor with 4x NVIDIA GeForce RTX 3090 (24 GB) GPUs.

Proof Stage
2^20 rows, 1135 columns
2^25 rows, 5 columns

Initialization

(6.04) 6.08

(1.40) 1.41

Generate Instance

(0.05) 0.05

(1.05) 1.05

Generate Advice

(381.78) 339.69

(6.68) 4.07

Generate Lookups

(57.99) 57.19

(2.10) 1.86

Commit Permutations

(146.59) 75.80

(23.72) 13.74

Eval_h

(1069.09) 1070.57

(66.55) 66.75

Compute Evaluations

(9.81) 7.49

(35.75) 6.10

Multiopen

(18.71) 18.94

(28.82) 11.61

Total

(1690.05) 1575.82

(166.10) 106.59

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