基于MILP的轻量级密码算法ACE与SPIX的线性分析  

Linear Analysis of Lightweight Cipher ACE and SPIX Based on Mixed-Integer Linear Programming

作　　者：刘帅 任小广 王世雄 关杰[3] 张啸川 谭捷 王军 LIU Shuai;REN Xiao-guang;WANG Shi-xiong;GUAN Jie;ZHANG Xiao-chuan;TAN Jie;WANG Jun(Intelligent Game and Decision Laboratory,Beijing 100091,China;Academy of Military Science,Beijing 100091,China;School of Cipher Engineering,SSF Information Engineering University,Zhengzhou,Henan 450001,China)

机构地区：[1]智能博弈与决策实验室,北京100091 [2]军事科学院,北京100091 [3]战略支援部队信息工程大学密码工程学院,河南郑州450001

出　　处：《电子学报》2024年第9期3065-3074,共10页Acta Electronica Sinica

基　　金：国家自然科学基金(No.62102440)。

摘　　要：研究了轻量级密码算法ACE与SPIX的线性性质.给出了环型与门组合结构精确的混合整数线性规划下的线性性质刻画,并将算法ACE与SPIX的非线性操作转化为环型与门组合.基于此构建了ACE置换与SLISCP置换的混合整数线性规划下的线性模型,求解模型得到了2至4步ACE置换与2至5步SLISCP置换最优的线性迹.证明了7步、12步ACE置换分别达到了128比特与320比特的安全目标,7步、13步SLISCP置换分别达到了128比特与256比特的安全目标.对于任意步数的ACE置换与SLISCP置换,认证加密算法ACE-AE-128与SPIX均能够抵抗明文处理阶段的线性区分攻击.The linear property of lightweight cipher ACE and SPIX was researched.The linear property of ring ANDgate combination was described accurately with mixed-integer linear programming.The nonlinear operation of ACE and SPIX was transformed into ring AND-gate combination.Based on this,the linear models of ACE permutation and SLISCP permutation were constructed with mixed-integer linear programming.The models returned the optimal linear characteris⁃tics of 2-step to 4-step ACE permutation and 2-step to 5-step SLISCP permutation.It was proved that 7-step and 12-step ACE permutation achieved the 128-bit security and 320-bit security respectively,and 7-step and 13-step SLISCP permuta⁃tion achieved the 128-bit security and 256-bit security respectively.For the ACE permutation and SLISCP permutation with any number of steps,authenticated encryption algorithm ACE-AE-128 and SPIX can resist the linear distinguish attack of plaintext processing stage.

关 键 词：混合整数线性规划 约束求解 轻量级密码算法 线性分析 

分 类 号：TN918.1[电子电信—通信与信息系统]