With the tremendous growth of technology, providing data security to critical applications such as smart grid, health care, and military is indispensable. On the other hand, due to the proliferation of external data threats in these applications, the loss incurred is incredibly high. Standard encryption algorithms such as RSA, ElGamal, and ECC facilitate in protecting sensitive data from outside attackers; however, they cannot perform computations on sensitive data while being encrypted. To perform computations and to process encrypted query on encrypted data, various homomorphic encryption (HE) schemes are proposed. Each of the schemes has its own shortcomings either related to performance or with storage that acts as the barrier for applying in real-time applications. With that conception, our objective is to design HE schemes that are simple by design, efficient in performance, and highly unimpeachable against attacks. Our first proposed scheme is based on Carmichael's Theorem, referred to as Carmichael's Theorem-based Homomorphic Encryption (CTHE), and the second is an improved version of Gorti's Enhanced Homomorphic Encryption Scheme, referred to as Modified Enhanced Homomorphic Encryption (MEHE). For brevity, the schemes are referred to as CTHE and MEHE. Both the schemes are provably secure under the hardness of integer factorization, discrete logarithm, and quadratic residuosity problems. To reduce the noise in these schemes, the modulus switching method is adopted and proved theoretically. The schemes' efficiency is proven by collecting the data from cardiovascular dataset (statically)/blood pressure monitor (dynamically) and is homomorphically encrypted in the edge server. Further analysis on encrypted data is carried out to identify whether a person has hypotension or hypertension with the aid of parameters, namely, mean arterial pressure. As the schemes are probabilistic in nature, breaking the schemes by a polynomial time adversary is impossible and is proven in the article.

中文翻译：

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在边缘计算系统中使用基于 Carmichael 定理的同态加密和改进的增强同态加密方案来保护医疗保健数据的安全和隐私

随着技术的飞速发展，为智能电网、医疗保健和军事等关键应用提供数据安全必不可少。另一方面，由于这些应用程序中外部数据威胁的扩散，造成的损失非常高。RSA、ElGamal 和 ECC 等标准加密算法有助于保护敏感数据免受外部攻击者的侵害；但是，它们在加密时无法对敏感数据执行计算。为了对加密数据执行计算和处理加密查询，提出了各种同态加密（HE）方案。每种方案都有其自身的缺点，要么与性能有关，要么与作为应用在实时应用程序中的障碍的存储有关。有了这样的构想，我们的目标是设计出设计简单、性能高效且对攻击无懈可击的 HE 方案。我们提出的第一个方案是基于 Carmichael 定理，称为基于 Carmichael 定理的同态加密 (CTHE)，第二个是 Gorti 的增强同态加密方案的改进版本，称为改进的增强同态加密 (MEHE)。为简洁起见，这些方案被称为 CTHE 和 MEHE。在整数分解、离散对数和二次剩余问题的困难下，这两种方案都被证明是安全的。为了降低这些方案中的噪声，采用模数切换方法并在理论上进行了验证。方案' 通过从心血管数据集（静态）/血压监测器（动态）收集数据来证明效率，并在边缘服务器中进行同态加密。对加密数据进行进一步分析，以借助参数（即平均动脉压）识别一个人是否患有低血压或高血压。由于这些方案本质上是概率性的，因此不可能通过多项式时间对手来破坏这些方案，并且在文章中得到了证明。