Several combined attacks have shown promising results in recovering cryptographic keys by introducing collision information into divide-and-conquer attacks to transform a part of the best key candidates within given thresholds into a much smaller collision space. However, these Collision-Optimized Divide-and-Conquer Attacks (CODCAs) uniformly demarcate the thresholds for all sub-keys, which is unreasonable. Moreover, the inadequate exploitation of collision information and backward fault tolerance mechanisms of CODCAs also lead to low attack efficiency. Finally, existing CODCAs mainly focus on improving collision detection algorithms but lack theoretical basis. We exploit Correlation-Enhanced Collision Attack (CECA) to optimize Template Attack (TA). To overcome the above-mentioned problems, we first introduce guessing theory into TA to enable the quick estimation of success probability and the corresponding complexity of key recovery. Next, a novel Multiple-Differential mechanism for CODCAs (MD-CODCA) is proposed. The first two differential mechanisms construct collision chains satisfying the given number of collisions from several sub-keys with the fewest candidates under a fixed probability provided by guessing theory, then exploit them to vote for the remaining sub-keys. This guarantees that the number of remaining chains is minimal, and makes MD-CODCA suitable for very high thresholds. Our third differential mechanism simply divides the key into several large non-overlapping “blocks” to further exploit intra-block collisions from the remaining candidates and properly ignore the inter-block collisions, thus facilitating the later key enumeration. The experimental results show that MD-CODCA significantly reduces the candidate space and lowers the complexity of collision detection, without considerably reducing the success probability of attacks.

中文翻译：

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碰撞优化分治攻击的多重差分机制


几种组合攻击通过将冲突信息引入分而治之的攻击中，将给定阈值内的部分最佳密钥候选转换为更小的冲突空间，在恢复加密密钥方面显示出了有希望的结果。然而，这些碰撞优化分治攻击（CODCA）统一划定所有子密钥的阈值，这是不合理的。此外，CODCA对碰撞信息的充分利用和后向容错机制也导致攻击效率低下。最后，现有的CODCA主要致力于改进碰撞检测算法，但缺乏理论基础。我们利用相关增强碰撞攻击（CECA）来优化模板攻击（TA）。为了克服上述问题，我们首先将猜测理论引入到TA中，以能够快速估计成功概率和相应的密钥恢复复杂度。接下来，提出了一种新颖的 CODCA 多微分机制（MD-CODCA）。前两种差分机制在猜测理论提供的固定概率下，从具有最少候选者的几个子密钥中构造满足给定碰撞次数的碰撞链，然后利用它们来投票给剩余的子密钥。这保证了剩余链的数量最少，并使 MD-CODCA 适合非常高的阈值。我们的第三种差分机制只是将密钥划分为几个大的不重叠的“块”，以进一步利用剩余候选者的块内冲突，并适当地忽略块间冲突，从而有利于后面的密钥枚举。 实验结果表明，MD-CODCA显着减少了候选空间，降低了碰撞检测的复杂度，而没有显着降低攻击的成功概率。