Paper 2022/1396 Original: eprint.iacr.org/2022/1396 ↗

FPGA Acceleration of Multi-Scalar Multiplication: CycloneMSM

Abstract

Multi-Scalar Multiplication (MSM) on elliptic curves is one of the primitives and bottlenecks at the core of many zero-knowledge proof systems. Speeding up MSM typically results in faster proof generation, which in turn makes ZK-based applications practical. We focus on accelerating large MSM on FPGA, and we present speed records for $\texttt{BLS12-377}$ on FPGA: 5.66s for $N=2^{26}$, sub-second for $N=2^{22}$. We developed a fully-pipelined curve adder in extended Twisted Edwards coordinates that runs at 250MHz. Our architecture incorporates a scheduler to reorder curve operations, that's suitable not just for hardware acceleration, but also for software implementations using affine coordinates with batch inversion. The software implementation achieves +$10-20$\% performance improvement over the state-of-the-art $\texttt{gnark-crypto}$ library.