一种基于二维离散忆阻超混沌映射的增强型密钥扩展算法  

Improved Key Expansion Algorithm Based on a 2D Discrete Hyper Chaotic Map with Memristor

作　　者：林哲 刘红军 LIN Zhe;LIU Hongjun(University of Jinan,School of Mathematical Science,Jinan 250022,China)

机构地区：[1]济南大学数学科学学院,济南250022

出　　处：《小型微型计算机系统》2024年第10期2537-2543,共7页Journal of Chinese Computer Systems

基　　金：山东省自然科学基金项目(ZR2022MF232)资助.

摘　　要：密钥扩展在对称分组密码中起着重要的作用,但AES和SM4等串行密钥扩展算法是可逆且串行的,所生成的轮密钥之间缺少独立性.本文通过设计一个增强型密钥扩展算法生成期望数量的轮密钥,且满足不可逆性、并行性以及轮密钥之间的独立性.首先,通过在2维离散超混沌映射(2D-DCM)中添加一个忆阻器,构造一个基于忆阻器的2维离散超混沌映射(2D-MDCM),该映射的状态点在相空间中具有遍历性,在足够大的参数范围内具有良好的随机性.基于2D-MDCM设计一个强S盒,该S盒没有不动点、反不动点以及短周期环.利用混沌迭代的不可逆性以及S盒,设计一种不可逆的密钥扩展算法,该算法可以并行生成指定轮数且灵活长度的轮密钥,每轮轮密钥都可以由初始密钥独立生成.实验和分析结果表明,改进后的密钥扩展算法大大提高了初始密钥的安全性.Key expansion plays an important role in symmetric block cipher,however,the AES and SM4 key expansion algorithms are reversible and serial,resulting in a lack of independence between the generated round keys.This article proposed the development of an enhanced key expansion algorithm that generated the desired number of round keys while ensuring irreversibility,parallelism,and independence among the round keys.First,we constructed a 2D memristor-based discrete hyper chaotic map(2D-MDCM),through adding a memristor to the 2D discrete hyper chaotic map(2D-DCM),whose state point has ergodicity in phase space and good randomness in a sufficiently large parameter range.We also constructed a strong S-Box without fixed point,reverse fixed point or short period ring based on 2D-MDCM.Took advantage of the irreversibility of the chaotic iteration and S-Box,we designed an irreversible key expansion algorithm,which can generate the round keys in parallel with specified round and flexible length,what′s more,each round key can be generated by the initial key independently.Experimental and analysis results demonstrated that the improved key expansion algorithm enhanced the security of initial key greatly.

关 键 词：忆阻混沌映射 S盒 密钥扩展 不可逆性 并行性 独立性 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]