(2026-06) Efficient Parallelization of Large-Scale Modular Multiplication via Low-Latency LogJumps
2026-06-26
Elliptic-Curve Cryptography (ECC) found in Zero-Knowledge Proofs (ZKPs) protects assets worth more than a billion dollars on privacy-preserving blockchain networks. There, the transaction rate is mostly limited by the computational cost of Multi-Scalar Multiplications (MSMs). Thus, hardware acceleration of these operations, for instance, using FPGAs, is of interest. Current accelerators leverage the Pippenger algorithm to compute the MSMs. Due to data dependencies, the algorithm’s performance is affected by the latency of the internal modular multipliers. Typically, these multiplications are realized using Montgomery multipliers. A promising variant of this algorithm is LogJumps, which offers potential for parallelism and lower latency. This is achieved by reducing data dependencies within the Montgomery reduction. Yet, prior work has neither formalized nor explored a low-latency, hardware-friendly parallel realization of this method. We address this gap by formalizing parallelism in LogJumps and presenting the first practical, truly parallel LogJumps architecture for the BLS12-377 prime. Our modular multiplication design achieves up to 56% lower latency than the lowest-latency multiplier in the ZPRIZE 2022, while maintaining a 250 MHz frequency and throughput. Furthermore, we reduce the MSM latency by up to 1.85× using a full-point adder pipeline, while our logic consumption increases by only 1.32×.