The authors use the mixed-integer linear programming (MILP) technique for the automatic search for differential characteristics of LEA and HIGHT ciphers. They show that the MILP model of the differential property of modular addition with one constant input can be represented with a much lesser number of linear inequalities compared to the general case. Benefiting from this model for HIGHT block cipher, they can achieve a reduction of 112 r out of 480 r in the total number of linear constraints for the MILP model of r -round of HIGHT. This saving accelerates the searching process of HIGHT about twice as fast. They enjoy the MILP model to investigate the differential effect of these ciphers and provide a more accurate estimation for the differential probability. Their observations show that despite HIGHT, LEA exhibits a strong differential effect. The results gained by this method improve/extend the previous results as follows. For LEA block cipher, they found more efficient 12- and 13-round differentials whose probabilities are better than the best previous 12- and 13-round differentials for a factor of about 2 ⁶ and 2 ⁷ , respectively. In the case of HIGHT block cipher, they found new 12- and 13-round differentials, though with the same best-reported probabilities.

中文翻译：

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基于MILP的LEA和HIGHT分组密码的自动差分搜索

作者使用混合整数线性规划（MILP）技术来自动搜索LEA和HIGHT密码的差分特性。他们表明，与一般情况相比，具有一个恒定输入的模块化加法的微分性质的MILP模型可以用更少的线性不等式表示。得益于此模型的HIGHT分组密码，它们可以减少112 [R 在480中 [R MILP模型的线性约束总数 [R 一轮的高。这种节省使HIGHT的搜索过程加快了大约两倍。他们喜欢用MILP模型来研究这些密码的微分效应，并为微分概率提供更准确的估计。他们的观察表明，尽管具有HIGHT，LEA仍显示出强大的差分作用。通过此方法获得的结果将改进/扩展以前的结果，如下所示。对于LEA块密码，他们发现更有效的12-和13-轮差速器，其概率是比最好的前12和13轮差速器更好为约2的因子 ⁶和2 ⁷ 分别。在HIGH分组密码的情况下，尽管发现的概率相同，但他们发现了新的12和13轮差分。