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约减轮数分组密码LEA的差分分析

李艳俊 李寅霜 刘健 王克

李艳俊, 李寅霜, 刘健, 王克. 约减轮数分组密码LEA的差分分析[J]. 电子与信息学报, 2023, 45(10): 3737-3744. doi: 10.11999/JEIT221282
引用本文: 李艳俊, 李寅霜, 刘健, 王克. 约减轮数分组密码LEA的差分分析[J]. 电子与信息学报, 2023, 45(10): 3737-3744. doi: 10.11999/JEIT221282
LI Yanjun, LI Yinshuang, LIU Jian, WANG Ke. Differential Analysis of Reduced Rounds Block Cipher LEA[J]. Journal of Electronics & Information Technology, 2023, 45(10): 3737-3744. doi: 10.11999/JEIT221282
Citation: LI Yanjun, LI Yinshuang, LIU Jian, WANG Ke. Differential Analysis of Reduced Rounds Block Cipher LEA[J]. Journal of Electronics & Information Technology, 2023, 45(10): 3737-3744. doi: 10.11999/JEIT221282

约减轮数分组密码LEA的差分分析

doi: 10.11999/JEIT221282
基金项目: 北京高校“高精尖”学科建设项目(20210101Z0401)
详细信息
    作者简介:

    李艳俊:女,副教授,博士,研究方向为分组密码的设计与分析、密码协议设计与分析

    李寅霜:女,硕士生,研究方向为分组密码分析方法

    刘健:男,高级工程师,硕士,研究方向为网络与信息安全、商用密码应用安全性评估等

    王克:男,讲师,博士,研究方向为公钥密码的设计与分析

    通讯作者:

    李寅霜 511228211@qq.com

  • 中图分类号: TN918.1; TP309.2

Differential Analysis of Reduced Rounds Block Cipher LEA

Funds: The Advanced Discipline Construction Project of Beijing Universities (20210101Z0401)
  • 摘要: LEA算法是面向软件的轻量级加密算法,在2019年成为 ISO/IEC 国际标准轻量级加密算法,具有快速加密、占用运算资源少等优点。该文基于多条输入输出差分相同的路径计算了差分概率,首次对LEA-128进行了13轮和14轮的密钥恢复攻击;采用提前抛弃技术,分别在12轮和13轮差分特征后面添加了1轮,恢复了96 bit密钥;其中13轮的密钥恢复攻击数据复杂度为298个明文,时间复杂度为286.7次13轮LEA-128解密;14轮的密钥恢复攻击数据复杂度为2118个明文,时间复杂度为2110.6次14轮LEA-128解密。
  • 图  1  LEA的轮变换

    图  2  存在的差分向量模式

    图  3  模加差分特性的线性不等式刻画

    图  4  13轮密钥恢复攻击

    图  5  14轮密钥恢复攻击

    表  1  LEA-128攻击分析结果比较

    参考文献攻击方法区分器轮数攻击轮数时间复杂度数据复杂度
    [1]差分分析11122842100
    本文差分分析12/1313/14285.7/2110.6298/2118
    [1]不可能差分分析1012
    [1]零相关线性密码分析79
    [9]零相关线性密码分析9921272127
    [11]零相关线性密码分析10
    [1]积分分析69
    [12]积分分析7/8296/2118
    [13]积分分析8/91021202124
    [10]积分分析7296
    [1]飞去来器分析方法715
    [14]差分线性密码分析12
    下载: 导出CSV
    算法1 最优特征的差分概率
     输入:对于 r 轮密码的原始MILP模型。
     输出:最优特征的概率多项式。
     (1) 求解原始MILP模型并获得最优差分特征的概率 d
       $(\varDelta _{ {\text{in} } }^ * ,\varDelta _{ {\text{out} } }^ * )$;
     (2) 令 j = –1 ;
     (3) 重复:
     (4)  j = j + 1 ;
     (5)  将原始MILP模型中的输入输出差分设为$(\varDelta _{ {\text{in} } }^ * ,\varDelta _{ {\text{out} } }^ * )$;
     (6)  令原始MILP模型中的目标函数 = d + j
     (7)  求解模型和不同特征的数量值$ {p_j} $;
     (8) 直到${p_j}{2^{ - (d + j)} } \ge \displaystyle\sum\limits_{i = 0}^{j - 1} { {p_i}{2^{ - (d + i)} } }$;
     (9) 令N = j – 1;
     (10) 返回:概率多项式。
    下载: 导出CSV

    表  2  LEA算法的12轮差分特征及概率

    轮数$\Delta {X_0}$$ \Delta {X_{\text{1}}} $$\Delta {X_{\text{2}}}$$\Delta {X_{\text{3}}}$${\log _2}p$
    0C0000000C04000804040001040400012
    1800100008000000C40000004C0000000–13
    202001800820000008000000080010000–8
    300300100001000000000200002001800–4
    4000200000001FF000040010000300100–15
    500020000000200000002000000020000–25
    600000000000000000000000000020000–5
    700000000000000000000400000000000–1
    800000000000002000000080000000000–2
    900040000000000300000010000000000–5
    1008002000800000080000002000040000–7
    1100401110C40000000000800408002000–8
    1280222188222004008100140000401110–14
    下载: 导出CSV

    表  3  LEA算法的13轮差分特征及概率

    轮数$\Delta {X_0}$$ \Delta {X_{\text{1}}} $$\Delta {X_{\text{2}}}$$\Delta {X_{\text{3}}}$${\log _2}p$
    0C0000000C04000804040001040400012
    1800100008000000C40000004C0000000–13
    202001800820000008000000080010000–8
    300300100001000000000200002001800–4
    4000200000001FF000040010000300100–15
    500020000000200000002000000020000–25
    600000000000000000000000000020000–5
    700000000000000000000400000000000–1
    800000000000002000000080000000000–2
    900040000000000300000010000000000–5
    1008002000800000080000002000040000–7
    1100401110C40000000000800408002000–8
    1280222188222004008100140000401110–14
    130449114405190080102800A180222088–20
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-10-10
  • 修回日期:  2023-04-19
  • 网络出版日期:  2023-04-24
  • 刊出日期:  2023-10-31

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