Homomorphic Encryption (HE) is a set of powerful properties of certain cryptosystems that allow for privacy-preserving operation over the encrypted text. Still, HE is not widespread due to limitations in terms of efficiency and usability. Among the challenges of HE, scheme parametrization (i.e., the selection of appropriate parameters within the algorithms) is a relevant multi-faced problem. First, the parametrization needs to comply with a set of properties to guarantee the security of the underlying scheme. Second, parametrization requires a deep understanding of the low-level primitives since the parameters have a confronting impact on the precision, performance, and security of the scheme. Finally, the circuit to be executed influences, and it is influenced by, the parametrization. Thus, there is no general optimal selection of parameters, and this selection depends on the circuit and the scenario of the application. Currently, most of the existing HE frameworks require cryptographers to address these considerations manually. It requires a minimum of expertise acquired through a steep learning curve. In this paper, we propose a unified solution for the aforementioned challenges. Concretely, we present an expert system combining Fuzzy Logic and Linear Programming. The Fuzzy Logic Modules receive a user selection of high-level priorities for the security, efficiency, and performance of the cryptosystem. Based on these preferences, the expert system generates a Linear Programming Model that obtains optimal combinations of parameters by considering those priorities while preserving a minimum level of security for the cryptosystem. We conduct an extended evaluation where we show that an expert system generates optimal parameter selections that maintain user preferences without undergoing the inherent complexity of analyzing the circuit.

翻译：同态加密（Homomorphic Encryption, HE）是某些密码系统的重要特性集合，允许对加密文本进行隐私保护操作。然而，由于效率和可用性方面的限制，同态加密尚未得到广泛应用。在HE面临的诸多挑战中，方案参数化（即在算法中选择适当参数）是一个涉及多方面的关键问题。首先，参数化需要满足一组属性以确保底层方案的安全性；其次，由于参数对方案的精度、性能和安全性存在相互制约的影响，参数化需要深入理解底层基本原语；最后，待执行电路既影响参数化过程，又受参数化结果影响。因此，不存在通用的最优参数选择方案，参数选择取决于具体电路和应用场景。当前，多数现有HE框架需要密码学家手动处理这些考量，这要求具备通过陡峭学习曲线获取的专业知识。本文针对上述挑战提出统一解决方案：具体而言，我们设计了一个融合模糊逻辑与线性规划的专家系统。模糊逻辑模块接收用户对密码系统安全性、效率和性能的高层优先级选择，基于这些偏好，专家系统构建线性规划模型，在优先考虑用户偏好的同时保持密码系统最低安全等级，从而获得最优参数组合。通过广泛评估，我们证明该专家系统能在无需分析电路固有复杂性的情况下，生成满足用户偏好的最优参数选择。