Improved Meet-in-the-middle Attacks on Reduced-round E2
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摘要: E2算法是AES首轮征集的15个候选算法之一，具有优良的软硬件实现效率和较强的安全性。该文利用多重集和差分枚举技术，对E2算法进行中间相遇攻击。首先以E2-128为例，改进了已有的4轮中间相遇区分器，将5轮密钥恢复攻击预计算复杂度降低为${2^{31}}$次5轮算法加密。其次针对E2-256，将所得区分器向后增加两轮，构造了6轮中间相遇区分器，并实现了9轮中间相遇攻击，攻击所需的数据复杂度为${2^{105}}$个选择明文，存储复杂度为${2^{200}}$ Byte，时间复杂度为${2^{205}}$次9轮算法加密。与现有对E2算法的安全性分析结果相比，该文实现了对E2-256最长轮数的攻击。Abstract: E2 is one of the 15 candidate algorithms in the first round of AES, which has the characteristics of excellent software and hardware implementation efficiency and strong security. The meet-in-the-middle attacks on E2 are carried out in this paper by using multiset tabulation technique and differential enumeration technique. First, E2-128 is taken as an example to improve the existing 4-round meet-in-the-middle distinguisher, and the pre-computation complexity of 5-round key recovery attack is reduced to ${2^{31}}$ 5-round encryptions. Second, for E2-256, a 6-round distinguisher is constructed from the new 4-round distinguisher by extending two rounds backward, and then a 9-round meet-in-the-middle attack is presented, whose data complexity is ${2^{105}}$ chosen plaintexts, memory complexity is ${2^{200}}$ Byte, and time complexity is ${2^{205}}$ 9-round encryptions. Compared with the existing security analysis results of E2, the scheme achieves the longest number of attack rounds for E2-256.
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Key words:
- Block cipher /
- E2 /
- Meet-in-the-middle attack /
- Differential enumeration technique
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表 1 E2算法攻击结果对比
来源 攻击方法 算法版本 轮数 时间复杂度 预计算复杂度 数据复杂度 文献[13] 截断差分 E2-128/E2-128 $ 7/8 $ – – ${2^{91}}/{2^{94}}$ 文献[14] 不可能差分 E2-128/E2-256 $ 7/8 $ ${2^{115.5}}/{2^{214}}$ – ${2^{120}}/{2^{121}}$ 文献[15] 中间相遇攻击 E2-128 5 ${2^{48}}$ ${2^{48}}$ $ 14 $ 本文 中间相遇攻击 E2-128 5 ${2^{47.9}}$ ${2^{31}}$ $ 12 $ 本文 中间相遇攻击 E2-256 9 ${2^{205}}$ ${2^{200.6}}$ ${2^{105}}$ 
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