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对TweAES的相关调柄多重不可能差分攻击

蒋梓龙 金晨辉

蒋梓龙, 金晨辉. 对TweAES的相关调柄多重不可能差分攻击[J]. 电子与信息学报, 2023, 45(1): 344-352. doi: 10.11999/JEIT211147
引用本文: 蒋梓龙, 金晨辉. 对TweAES的相关调柄多重不可能差分攻击[J]. 电子与信息学报, 2023, 45(1): 344-352. doi: 10.11999/JEIT211147
JIANG Zilong, JIN Chenhui. Related-Tweak Multiple Impossible Differential Attack for TweAES[J]. Journal of Electronics & Information Technology, 2023, 45(1): 344-352. doi: 10.11999/JEIT211147
Citation: JIANG Zilong, JIN Chenhui. Related-Tweak Multiple Impossible Differential Attack for TweAES[J]. Journal of Electronics & Information Technology, 2023, 45(1): 344-352. doi: 10.11999/JEIT211147

对TweAES的相关调柄多重不可能差分攻击

doi: 10.11999/JEIT211147
基金项目: 国家自然科学基金(61772547, 61902428, 61802438)
详细信息
    作者简介:

    蒋梓龙:男,博士生,研究方向为分组密码设计与分析

    金晨辉:男,教授,博士生导师,研究方向为密码学和信息安全

    通讯作者:

    蒋梓龙 dracipher@126.com

  • 中图分类号: TN918.1

Related-Tweak Multiple Impossible Differential Attack for TweAES

Funds: The National Natural Science Foundation of China (61772547, 61902428, 61802438)
  • 摘要: TweAES算法是在NIST轻量级密码标准竞赛中,进入到第2轮的认证加密候选算法。该文提出了对8轮TweAES算法的相关调柄多重不可能差分攻击。首先,利用两类不可能差分区分器,构造了两条攻击路径,每条攻击路径需要攻击16 Byte子密钥。值得注意的是,两条攻击路径有相同的明文结构和14 Byte的公共子密钥,攻击者可以利用同一个明文结构下的明文对,筛选两次错误子密钥,且因为有大量的公共子密钥,可以提高子密钥筛选的效率。此外,利用密钥生成算法的不完全性,有针对性地选择子密钥字节。利用子密钥之间的相关性,提高主密钥恢复效率,从而改进整体攻击方案的结果。与前人的分析结果相比较,该文对8轮TweAES的攻击方案在时间、数据、存储3项复杂度结果上均有所改进。
  • 图  1  TweAES算法的轮函数图(偶数轮)

    图  2  TweAES算法的6轮相关调柄不可能差分区分器

    图  3  TweAES算法的8轮相关调柄不可能差分攻击路径

    表  1  符号说明

    符号意义
    $ P $明文
    $ C $密文
    $x_{i,(p,\cdots,r)}^{{\rm{I/SB/SR/MC/AK/AT}}}$第$ i $轮输入/字节替换/行移位变换/混合变换/轮密钥加/调柄加后的第$(p, \cdots ,r)$ Byte值
    $\Delta x$$x$的差分值
    ${k_{i,(p,\cdots,r)} }$第$ i $轮子密钥${k_i}$的第$(p, \cdots ,r)$ Byte值
    $a{\not \to _{i - {\rm{round}}} }b$差分$ a $经$ i $轮加密后不能得到差分$ b $
    下载: 导出CSV

    表  2  TweAES的8个6轮相关调柄不可能差分区分器

    类别序号区分器的输入差分(具体差分值)区分器的输入差分(截断差分值)
    1(a,a,0,0,0,0,0,0,0,0,0,0,a,a,0,0)(0,0,0,0,0,0,0,0,0,0,0,0,*,0,0,0)
    2(0,0,0,0,0,0,0,0,0,0,0,0,0,*,0,0)
    3(0,0,0,0,0,0,0,0,0,0,0,0,0,0,*,0)
    4(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,*)
    5(*,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0)
    6(0,*,0,0,0,0,0,0,0,0,0,0,0,0,0,0)
    7(0,0,*,0,0,0,0,0,0,0,0,0,0,0,0,0)
    8(0,0,0,*,0,0,0,0,0,0,0,0,0,0,0,0)
    注:a为8 bit具体值0x01,*为8 bit任意非零值。主调柄差分值为(1001)。
    下载: 导出CSV

    表  3  AES-128中第9轮子密钥后12 Byte与第1轮子密钥关联

    密钥字节关联字节密钥字节关联字节密钥字节关联字节
    4A16\{0,2,8,10}8A16\{0,1,4}12A16\{0,1,2,4,5,8,10}
    5A16\{1,3,9,11}9A16\{1,2,5}13A16\{1,2,3,5,6,9,11}
    6A16\{0,2,8,10}10A16\{2,3,6}14A16\{0,2,3,6,7,8,10}
    7A16\{1,3,9,11}11A16\{0,3,7}15A16\{0,1,3,4,7,9,11}
    注:密钥字节为第9轮子密钥字节位置,A16代表全部16 Byte,关联字节指与第1轮子密钥字节的关联:如$ {k_{9, (4)}} $与4 Byte子密钥$ {k_{1, (0,2,8,10)}} $无关,只需要知道子密钥$ {k_1} $其余的12 Byte,即可由AES-128的密钥生成算法得到。
    下载: 导出CSV

    表  4  TweAES的攻击结果

    分析方法轮数时间复杂度数据复杂度存储复杂度调柄个数参考文献
    截断差分522625 CP228.582[1]
    积分攻击624525 KP24[1]
    不可能差分621192119 CP278.172[1]
    不可能差分72100299 CP2702[20]
    不可能差分*821272127 CP29624[1]
    不可能差分82124.362124.28 CP2118.812[20]
    不可能差分82120.822122.10 CP21132本文
    CP:选择明文  KP:已知明文  –:复杂度较小忽略不计
    *:由文献[20]修正后,时间复杂度超出穷举攻击,本表列出的为文献[1]中所声称的复杂度。
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-10-21
  • 修回日期:  2022-03-21
  • 网络出版日期:  2022-04-15
  • 刊出日期:  2023-01-17

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