Paper 2026/521 Original: eprint.iacr.org/2026/521 ↗

UniMSM: An Efficient and Flexible Hardware Accelerator for Multi-Scalar Multiplication

Abstract

Multi-scalar multiplication (MSM) is a central kernel in cryptographic systems, which evaluates large linear combinations of elliptic-curve points. Practical MSMs couple millions of terms with hundreds-of-bit modular arithmetic, while Pippenger’s bucket flow introduces irregular memory updates that can severely degrade utilization under deep pipelines. In this paper, we present UniMSM, an efficient and flexible hardware accelerator for MSM across practical problem sizes and diverse curve parameters. First, we design a pipelined point adder based on the extended Jacobian coordinate system and employ a time-multiplexed datapath to reduce modular multiplier cost while sustaining high throughput. Second, we introduce a conflict-aware scheduling scheme to address bucket-update conflicts and preserve utilization under irregular accesses. Third, we develop a hardware-friendly variant of the Pippenger algorithm to reduce intermediate storage overhead and serial dependencies in aggregation. Compared with prior FPGA accelerators, UniMSM achieves up to 2.12$\times$ improvement in area-time product. Furthermore, UniMSM in ASIC achieves up to a 3.85$\times$ improvement in ATP compared to the SOTA accelerator.