Symmetric key cryptography stands as a fundamental cornerstone in ensuring security within contemporary electronic communication frameworks. The cryptanalysis of classical symmetric key ciphers involves traditional methods and techniques aimed at breaking or analyzing these cryptographic systems. In the evaluation of new ciphers, the resistance against linear and differential cryptanalysis is commonly a key design criterion. The wide trail design technique for block ciphers facilitates the demonstration of security against linear and differential cryptanalysis. Assessing the scheme's security against differential attacks often involves determining the minimum number of active SBoxes for all rounds of a cipher. The propagation characteristics of a cryptographic component, such as an SBox, can be expressed using Boolean functions. Mixed Integer Linear Programming (MILP) proves to be a valuable technique for solving Boolean functions. We formulate a set of inequalities to model a Boolean function, which is subsequently solved by an MILP solver. To efficiently model a Boolean function and select a minimal set of inequalities, two key challenges must be addressed. We propose algorithms to address the second challenge, aiming to find more optimized linear and non-linear components. Our approaches are applied to modeling SBoxes (up to six bits) and EXOR operations with any number of inputs. Additionally, we introduce an MILP-based automatic tool for exploring differential and impossible differential propagations within a cipher. The tool is successfully applied to five lightweight block ciphers: Lilliput, GIFT64, SKINNY64, Klein, and MIBS.

翻译：对称密钥密码学是现代电子通信框架中确保安全性的基本基石。经典对称密钥密码的密码分析涉及旨在破解或分析这些密码系统的传统方法和技术。在新密码的评估中，抵抗线性和差分密码分析通常是关键的设计标准。分组密码的宽轨迹设计技术有助于证明针对线性和差分密码分析的安全性。评估方案对差分攻击的抵抗力通常需要确定密码所有轮次中活跃S盒的最小数量。密码组件（如S盒）的传播特性可以用布尔函数表示。混合整数线性规划（MILP）被证明是求解布尔函数的一种有价值的技术。我们制定了一组不等式来建模布尔函数，随后由MILP求解器进行求解。为了有效建模布尔函数并选择最小不等式集合，必须解决两个关键挑战。我们提出了算法来应对第二个挑战，旨在找到更优化的线性和非线性组件。我们的方法应用于建模S盒（最多六位）和任意输入数量的异或运算。此外，我们引入了一种基于MILP的自动工具，用于探索密码中的差分和不可能差分传播。该工具成功应用于五种轻量级分组密码：Lilliput、GIFT64、SKINNY64、Klein和MIBS。