Homomorphic encryption is a sophisticated encryption technique that allows computations on encrypted data to be done without the requirement for decryption. This trait makes homomorphic encryption appropriate for safe computation in sensitive data scenarios, such as cloud computing, medical data exchange, and financial transactions. The data is encrypted using a public key in homomorphic encryption, and the calculation is conducted on the encrypted data using an algorithm that retains the encryption. The computed result is then decrypted with a private key to acquire the final output. This abstract notion protects data while allowing complicated computations to be done on the encrypted data, resulting in a secure and efficient approach to analysing sensitive information. This article is intended to give a clear idea about the various fully Homomorphic Encryption Schemes present in the literature and analyse and compare the results of each of these schemes. Further, we also provide applications and open-source tools of homomorphic encryption schemes.

翻译：同态加密是一种先进的加密技术，允许在不需解密的情况下对加密数据进行计算。这一特性使其适用于敏感数据场景下的安全计算，例如云计算、医疗数据交换和金融交易。在同态加密中，数据使用公钥进行加密，计算通过保留加密状态的算法在加密数据上执行，随后使用私钥对计算结果进行解密以获取最终输出。这一抽象概念在保护数据的同时，允许对加密数据进行复杂计算，从而为敏感信息的分析提供了一种安全高效的方法。本文旨在清晰阐述文献中存在的各种全同态加密方案，分析并比较各方案的性能结果。此外，我们还介绍了同态加密方案的应用场景及开源工具。