| 摘要: |
| 研究3类非平衡广义Feistel结构的中间相遇攻击, 并在Q1模型下对这3类结构进行量子中间相遇攻击. 首先, 采用多重集和差分枚举技术对3分支Type-III型广义Feistel结构构建4轮中间相遇区分器, 分别向前向后扩展1轮进行6轮中间相遇攻击, 并利用Grover算法和量子爪搜索算法对该结构进行6轮量子密钥恢复攻击, 该攻击所需的时间复杂度为O(23l/2·l)次量子查询, 其中l为广义Feistel结构的分支长度. 其次, 对3分支Type-I型广义Feistel结构的9轮区分器分别向前向后扩展1轮进行11轮中间相遇攻击及量子密钥恢复攻击, 相应的时间复杂度分别为O(22l)次11轮加密和O(23l/2·l)次量子查询. 最后, 以 3-cell型广义Feistel结构为例探讨了n-cell型广义Feistel结构的量子中间相遇过程, 对n-cell型广义Feistel结构构建2n轮中间相遇区分器, 并进行2(n+1)轮中间相遇攻击及量子密钥恢复攻击, 且时间复杂度分别为O(22l)次2(n+1)轮加密和O(23l/2·l)次量子查询. 结果表明, 相比于经典环境, Q1模型下消耗的时间复杂度更低. |
| 关键词: 广义 Feistel结构 量子中间相遇攻击 Q1 模型 量子爪搜索算法 Grover算法 |
| DOI：10.13328/j.cnki.jos.007448 |
| 分类号:TP309 |
| 基金项目:国家自然科学基金(62172337); 甘肃省自然科学基金重点项目(23JRRA685); 甘肃省基础研究创新群体基金(23JRRA684) |
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| Quantum Meet-in-the-middle Attacks on Three Types of Unbalanced Generalized Feistel Structures |
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DU Xiao-Ni1,2, WU Jia-Hui1, XU Ying1, SUN Rui1
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1.College of Mathematics and Statistic, Northwest Normal University, Lanzhou 730070, China;2.Key Laboratory of Cryptography and Data Analytics, Northwest Normal University, Lanzhou 730070, China
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| Abstract: |
| This study investigates meet-in-the-middle attacks on three types of unbalanced generalized Feistel structures and conducts quantum meet-in-the-middle attacks in Q1 model. First, for the 3-branch Type-III generalized Feistel structure, a 4-round meet-in-the-middle distinguisher is constructed using multiset and differential enumeration techniques. By expanding one round forward and one round backward, a 6-round meet-in-the-middle attack is conducted. With the help of Grover’s algorithm and the quantum claw finding algorithm, a 6-round quantum key recovery attack is performed, requiring O(23l/2·l) quantum queries, where l is the branch length of the generalized Feistel structure. Then, for the 3-branch Type-I structure, a 9-round distinguisher is similarly extended by one round in both directions to conduct an 11-round meet-in-the-middle attack and a quantum key recovery attack with time complexities of O(22l) 11-round encryptions and O(23l/2·l) quantum queries. Finally, taking the 3-cell generalized Feistel structure as a representative case, this study explores a quantum meet-in-the-middle attack on an n-cell structure. A 2n-round meet-in-the-middle distinguisher is constructed, enabling a 2(n+1)-round meet-in-the-middle attack and quantum key recovery attack. The associated time complexities are O(22l) 2(n+1)-round encryptions and O(23l/2·l) quantum queries. The results demonstrate that the time complexity in Q1 model is significantly reduced compared with classical scenarios. |
| Key words: generalized Feistel structure quantum meet-in-the-middle attack Q1 model quantum claw finding algorithm Grover’s algorithm |
