密码学报（中英文）2025，Vol.12Issue(4)：854-869,16.DOI:10.13868/j.cnki.jcr.000798
基于正规基的大规模S盒FPGA设计与实现
FPGA Design and Implementation of Large-Scale S-Boxes Based on Normal Basis
摘要
Abstract
Traditional hardware implementation of block cipher S-boxes typically uses table lookup method,and its performance is constrained by chip resources.To address the issue of high resource consumption in FPGA hardware implementation of 16-bit large-scale S-boxes,this study proposes a construction method for S-boxes based on normal basis in composite fields,aiming to implement 16-bit S-boxes with reduced hardware resource usage.First,a construction scheme for a 16-bit S-box based on composite fields is designed,and linear isomorphism matrices and their inverse matrices are constructed.Next,using the mapping matrix,the multiplication inverse of the finite field GF(216)is transformed to the composite field GF((((22)2)2)2),thereby simplifying the nonlinear high-dimensional multiplication inverse to low-dimensional subfield operations.Then,the optimal parameters are se-lected by analyzing the impact of different parameters in each level of the composite field on the S-box implementation.Finally,using the proposed 16-bit S-box construction framework,FPGA sim-ulation and performance analysis are carried out using the 16-bit S-box of the MK-3 algorithm as an example,utilizing Xilinx Vivado development tools.The results show that the MK-3 algorithm S-box implemented with the proposed method requires 186 LUTs,with a clock frequency of 114.129 MHz,achieving a performance metric of 0.613 60 in terms of clock frequency per LUT.Compared to the optimal implementation performance of 0.435 38 in existing literature,this method improves performance by 40.93％.The proposed 16-bit S-box implementation scheme can maintain a high oper-ating frequency for cryptographic algorithms while reducing hardware resource consumption,offering valuable reference for the efficient soft and hardware implementation of S-boxes based on finite field constructions.关键词
大规模S盒/复合域/正规基/MK-3算法/FPGAKey words
large-scale S-boxes/composite field/normal basis/MK-3 algorithm/FPGA分类
信息技术与安全科学引用本文复制引用
张磊,李国元,洪睿鹏,王建新,肖超恩..基于正规基的大规模S盒FPGA设计与实现[J].密码学报（中英文）,2025,12(4):854-869,16.基金项目
处理器芯片全国重点实验室开放课题(CLQ202516) （CLQ202516）
中央高校基本科研业务费资金(3282024009,3282024051)State Key Lab of Processors(CLQ202516) （3282024009,3282024051）
The Fundamental Research Funds for the Central Univer-sities of China(3282024009,3282024051) （3282024009,3282024051）
