MMzk: 384-bit Low-Resource Montgomery Multiplier on FPGA for zk-SNARK

Abstract

Zero-Knowledge Proof (ZKP) is a privacy-preserving protocol that allows a prover to demonstrate the validity of a statement without revealing its details. A widely used primitive of ZKP, Zero-Knowledge Succinct Non-Interactive Argument of Knowledge (zk-SNARK), has attracted significant attention in edge computing; however, edge devices face severe resource constraints when processing its computational bottleneck, Montgomery multiplication. This paper proposes MMzk, a lightweight hardware architecture optimized for 384-bit Coarsely Integrated Operand Scanning (CIOS) Montgomery multiplication, which is primarily employed in multi-scalar multiplication (MSM) of zk-SNARKs. To achieve both high performance and resource efficiency, MMzk core operating at the System-on-Chip (SoC) level integrates three key optimizations: resource sharing of two adders, a subtractor, and a multiplier; effective memory organization for large-data processing; and double-buffering memory scheduling. Implementation results on a Xilinx ZCU102 SoC show that MMzk core operates at up to 250MHz with a utilization of 3,590 LUTs, 1,648 FFs, 16 DSPs, and 6 BRAM36 blocks. Compared with existing FPGA-based counterparts, it achieves a throughput of 657.53Mbps (up to 35.9 times higher) and an area efficiency of 81.48Kbps/eLUT (up to 9.5 times higher). Furthermore, real-time evaluation demonstrates an energy efficiency of 9,030Mbps/W at 250MHz and 67mW, surpassing modern CPUs by up to 52.9 times. These results confirm MMzk core as an energy-efficient and high-performance solution for zk-SNARK-based blockchain systems and other Montgomery multiplication applications.