Zero-Knowledge Proof (ZKP) has gained widespread application across various domains, demonstrating remarkable success. Among ZKP algorithms, Zero-Knowledge Succinct Non-Interactive Argument of Knowledge (zk-SNARK) is the most widely used. However, despite its advantages of small proof size and succinct verification, zk-SNARK proof generation faces significant challenges due to high computational demands, limiting its practical application. This paper addresses these challenges by accelerating two computationally intensive operations in zk-SNARK proof generation, Number Theory Transformation (NTT) and Multi-Scalar Multiplication (MSM), using FPGAs. In the implementation of NTT hardware accelerators for zk-SNARK applications, the traditional 4-step algorithm often encounters conflicts between off-chip bandwidth and on-chip memory. To resolve this issue, we propose an innovative approach that enhances accelerator performance by recursively applying the 4-step algorithm to create a more efficient 6-step algorithm. For MSM hardware acceleration on FPGAs, existing works are often constrained by limited on-chip memory, restricting the use of longer slice lengths, which are crucial for higher performance when using the commenly used Pippenger algorithm. To overcome this limitation, we introduce the Batch Method, optimizing off-chip memory consumption, enabling the accelerator to use longer slice lengths and achieve superior performance. Experimental results demonstrate that the proposed NTT design achieves 1.76× higher DSP efficiency than the SAM. Meanwhile, the proposed MSM design demonstrates 1.24× higher performance than the MSMAC with aligned frequency and number of PEs. When benchmarked against the GPU implementation GZKP, our MSM design exhibits 1.16× and 1.46× higher performance than GZKP for BLS12-381 and BN-254, respectively. However, the NTT design remains at a disadvantage due to the bandwidth limitation between our platform, Xilinx Alveo U250, and GZKP’s platforms, Nvidia GTX 1080 Ti and Nvidia Tesla V100.

With the growth of field-programmable gate array (FPGA) hardware resources, streaming DCNN accelerators leverage interconvolutional-layer parallelism to enhance throughput. In existing streaming accelerators, convolution nodes typically adopt layer- or column-based tiling methods, where the tiled input feature map (Ifmap) encompasses all input channels. This approach facilitates the comprehensive calculation of the output feature map (Ofmap) and maximizes interlayer parallelism. The computational granularity, defined in this study as the calculated rows or columns of Ofmap based on each tiled Ifmap data, significantly influences on-chip Ifmap storage and off-chip weight bandwidth (BW). The uniform application of computational granularity across all nodes inevitably impacts the memory-BW tradeoff. This article introduces a novel streaming accelerator with a hybrid computational granularity (HCG) scheme. Each node employs an independently optimized computational granularity, enabling a more flexible memory-BW tradeoff and more effective utilization of FPGA resources. However, this hybrid scheme can introduce pipeline bubbles and increase system pipeline complexity and control logic. To address these challenges, this article theoretically analyzes the impact of computational granularity on individual computing nodes and the overall system, aiming to establish a seamless system pipeline without pipeline bubbles and simplify system design. Furthermore, the article develops a hardware overhead model and employs a heuristic algorithm to optimize computational granularity for each computing node, achieving optimal memory-BW tradeoff and higher throughput. Finally, the effectiveness of the proposed design and optimization methodology is validated through the implementation of a 3-TOPS ResNet-18 accelerator on the Alveo U250 development board under BW constraints of 25, 20, and 15 GB/s. Additionally, accelerators for 4-TOPS VGG-16, 4-TOPS ResNet-34, 5-TOPS ResNet-50, 3-TOPS MobileNetV1, 4-TOPS ConvNeXt-T, and 4-TOPS ResNeXt-50 are implemented, surpassing the performance of most existing works.

The field-programmable gate array (FPGA)-based CNN hardware accelerator adopting single-computing-engine (CE) architecture or multi-CE architecture has attracted great attention in recent years. The actual throughput of the accelerator is also getting higher and higher but is still far below the theoretical throughput due to the inefficient computing resource mapping mechanism and data supply problem, and so on. To solve these problems, a novel composite hardware CNN accelerator architecture is proposed in this article. To perform the convolution layer (CL) efficiently, a novel multiCE architecture based on a row-level pipelined streaming strategy is proposed. For each CE, an optimized mapping mechanism is proposed to improve its computing resource utilization ratio and an efficient data system with continuous data supply is designed to avoid the idle state of the CE. Besides, to relieve the off-chip bandwidth stress, a weight data allocation strategy is proposed. To perform the fully connected layer (FCL), a single-CE architecture based on a batch-based computing method is proposed. Based on these design methods and strategies, visual geometry group network-16 (VGG-16) and ResNet-101 are both implemented on the XC7VX980T FPGA platform. The VGG-16 accelerator consumed 3395 multipliers and got the throughput of 1 TOPS at 150 MHz, that is, about 98.15% of the theoretical throughput ( 2 ×3395 ×150 MOPS). Similarly, the ResNet-101 accelerator achieved 600 GOPS at 100 MHz, about 96.12% of the theoretical throughput ( 2 ×3121 ×100 MOPS).