Authors: Yutian Chen, Cong Peng, Yu Dai, Min Luo, Debiao He

Title: Load-Balanced Parallel Implementation on GPUs for Multi-Scalar Multiplication Algorithm

Conference: The 26th annual Conference on Cryptographic Hardware and Embedded Systems (CHES)

Abstract: . Multi-scalar multiplication is an important building block in most of elliptic-curve-based zero-knowledge proof systems, such as Groth16 and PLONK. Recently, Lu et al. proposed cuZK, a new parallel multi-scalar multiplication algorithm on GPUs. In this paper, we revisit this scheme and present a new GPU-based implementation to further improve the performance of multi-scalar multiplication algorithm. First, we propose a novel method for mapping scalars into Pippenger’s bucket indices, largely reducing the number of buckets compared to the original Pippenger algorithm. Second, in the case that memory is sufficient, we develop a new efficient algorithm based on homogeneous coordinates in the bucket accumulation phase. Moreover, our accumulation phase is load-balanced, which means the parallel speedup ratio is almost linear growth as the number of device threads increases. Finally, we also propose a parallel layered reduction algorithm for the bucket aggregation phase, whose time complexity remains at the logarithmic level of the number of buckets. The implementation results over the BLS12-381 curve on the V100 graphics card show that our proposed algorithm achieves up to 1.998×, 1.821× and 1.818× speedup compared to cuZK at scales of 2^21 , 2^22, and 2^23, respectively.