A High-Speed Architecture for the Reduction in VDF Based on a Class Group

Abstract

Due to the enormous energy consuming involved in the proof of work (POW) process, the resource-efficient blockchain system is urged to be released. The verifiable delay function (VDF), being slow to compute and easy to verify, is believed to be the kernel function of the next-generation blockchain system. In general, the reduction over a class group, involving many complex operations, such as the large-number division and multiplication operations, takes a large portion in the VDF. In this paper, for the first time, we propose a highspeed architecture for the reduction by incorporating algorithmic transformations and architectural optimizations. Firstly, based on the fastest reduction algorithm, we present a modified version to make it more hardware-friendly by introducing a novel transformation method that can efficiently remove the large-number divisions. Secondly, highly parallelized and pipelined architectures are devised respectively for the large-number multiplication and addition operations to reduce the latency and the critical path. Thirdly, a compact state machine is developed to enable maximum overlapping in time for computations. The experiment results show that when computing 209715 reduction steps with the input width of 2048 bits, the proposed design only takes 137.652ms running on an Altera Stratix-10 FPGA at 100MHz frequency, while the original algorithm needs 3278ms when operating over an i7-6850K CPU at 3.6GHz frequency. Thus we have obtained a drastic speedup of nearly 24x over an advanced CPU.