Faster Montgomery multiplication and Multi-Scalar-Multiplication for SNARKs

The bottleneck in the proving algorithm of most elliptic-curve-based SNARK proof systems is Multi-Scalar-Multiplication (MSM) algorithm. In this paper we give an overview a variant Pippenger MSM together with set optimizations tailored for curves that admit twisted Edwards form. We prove case SNARK-friendly chains and cycles elliptic curves, which are useful recursive constructions. Our contribution twofold: first, optimize arithmetic finite fields by improving on well-known Coarsely Integrated Operand Scanning (CIOS) modular multiplication. This independent interest applies to many different contexts. Second, propose new coordinate system algorithm.Accelerating over these critical deployment proof< applications such as proof-carrying-data, blockchain rollups light clients. implement our work Go benchmark it two CPU architectures (x86 arm64). show implementation achieves 40-47% speedup state-of-the-art (which was implemented Rust). won first place ZPrize competition open division “Accelerating Mobile” will be deployed real-world applications: Linea zkEVM ConsenSys probably Celo network.