Homomorphic encryption (HME) is a sophisticated encryption technique that allows computations on encrypted data to be done without the requirement for decryption. This trait makes HME, appropriate for safe computation in scenarios involving sensitive data and also in cloud computing. The data is encrypted using a public key and the calculation is conducted on the encrypted data. The computed result is then decrypted with a private key to acquire the final output. It protects data while allowing complicated computations to be done on the encrypted data, resulting in a secure and efficient approach to analyse sensitive information. The ability of HME to do computations on encrypted data without decryption makes it a valuable tool for achieving privacy. This chapter is intended to give a clear idea about the various fully HME schemes present in the literature, as well as analysing and comparing the results of each of these schemes. The authors also provide applications and open-source tools of HME schemes, along with how HME can be used to establish and preserve privacy in various forms.
Top1. Introduction
The term “homomorphic” is derived from two Greek roots: “homo,” which means “same,” and “morph,” which means “shape.” The term homomorphism in mathematics refers to a structure-preserving map between two algebraic systems whose operations are the same or similar. The phrase “homomorphic encryption” refers to how this encryption approach allows computations to be conducted on encrypted data while preserving the data's structure, allowing the same computations to be performed on encrypted data as on unencrypted data. Homomorphic Encryption (HE) is a kind of encryption scheme that allows a third party (e.g., cloud, service provider) to perform certain computable functions on the encrypted data while preserving the features of the function and format of the encrypted data.
Encryption methods like RSA, AES, and DES are not homomorphic, meaning that they require the data to be decrypted before any computation can be performed. This makes it challenging to use these encryption methods in situations where data privacy is a critical concern, such as cloud computing and data analytics. In contrast, homomorphic encryption enables computations to be performed directly on encrypted data, without the need for decryption. This has significant implications for privacy-preserving technologies, as it allows for secure outsourcing of computation to untrusted servers, while maintaining the confidentiality of the data. Moreover, RSA, AES, and DES can be used for other aspects of security, such as key management and message authentication.
Privacy is a fundamental human right and refers to a person's ability to govern their own information, decisions, and activities, as well as defend themselves against unauthorised access or observation. Privacy can take different forms. Informational privacy means protecting personal information and having the right to decide how it is collected, used, and shared. Physical privacy is a person's right to be alone and not have other people touch them. Communication privacy has to do with keeping private talks and electronic messages private. In a variety of situations, including healthcare, banking, technology, and government, privacy plays a critical role in developing trust and creating a sense of security.
People often confuse the terms privacy and confidentiality (Folkman, 2000). Privacy is a broader notion that includes the control and protection of personal information as well as autonomy, whereas confidentiality focuses on the protection of specific sensitive information as well as the need to keep it confidential. While the former is a fundamental right that applies to many elements of a person's life, the latter is a principle or agreement that is implemented in certain settings to ensure the protection of sensitive data or information.
Data privacy, computing privacy, and communication privacy are all interconnected and necessary for securing personal information, preserving individual rights, and establishing trust in the digital domain. The ability of FHE to do computations on encrypted data without decryption makes it a valuable tool for achieving privacy. It protects data security, enables secure outsourcing, maintains privacy during computing, limits data exposure, conforms with rules, and promotes trust in third-party services. FHE creates new opportunities for privacy-preserving technologies and applications across multiple domains, contributing to a more privacy-conscious and secure digital ecosystem.
Unlike other review papers (Acar et al., 2018) in the literature, which typically provide a high-level overview of different FHE schemes, this paper goes a step further by providing a simple and step-by-step algorithm for each of the FHE schemes discussed. This makes the FHE schemes more accessible to a wider audience, including those who may not have a deep background in cryptography or computer science. By breaking down the algorithms into simple steps, readers can follow along and understand how the scheme works at a more fundamental level.