The integral cryptanalysis is a powerful cryptanalytic technique for the security evaluation of block cipher. However, when using the MILP-aided division property to search the integral distinguishers, many candidates of initial division properties need to be tested, so that the computations are unbearable in practice. This study takes advantage of the division property propagation of S-box to improve the optimal integral distinguisher searching algorithm, and further reduce its time complexity. Whereafter, the improved algorithm is used to give 8- and 9-round integral distinguishers of uBlock-128 and uBlock-256, and 10- and 9-round integral distinguishers of Pyjamask-96 and Pyjamask-128. On this basis, utilising the partial sums technique, the authors perform 9- and 11-round key-recovery attacks on uBlock-128 and Pyjamask-96, respectively. The data complexities are and , and the time complexities are less than times of 9-round uBlock-128 encryption and times of 11-round Pyjamask-96 encryption. The results given in this study are the best integral attacks available of the two ciphers presently.

中文翻译：

---

对两个块密码Pyjamask和uBlock进行积分密码分析

积分密码分析是用于分组密码安全性评估的强大密码分析技术。但是，当使用MILP辅助的除法属性搜索积分区分符时，需要测试许多初始除法属性的候选对象，因此在实践中无法进行计算。这项研究利用S-box的分割属性传播来改进最佳积分判别器搜索算法，并进一步降低其时间复杂度。此后，使用改进的算法给出uBlock-128和uBlock-256的8和9轮积分标识符，以及Pyjamask-96和Pyjamask-128的10和9轮积分标识符。在此基础上，利用偏和技术，作者分别对uBlock-128和Pyjamask-96进行了9轮和11轮密钥恢复攻击。 和 ，并且时间复杂度小于 9轮uBlock-128加密的时间和 11轮Pyjamask-96加密的时间。这项研究给出的结果是目前两个密码中最好的整数攻击方法。