what is homomorphic encryption

Homomorphic encryption is a form of encryption that allows computations to be performed on encrypted data without first having to decrypt it. The resulting computations are left in an encrypted form which, when decrypted, result in an output that is identical to that produced had the operations been performed on the unencrypted data. Homomorphic encryption can be used for privacy-preserving outsourced storage and computation. It allows data to be encrypted and out-sourced to commercial cloud environments for processing, all while encrypted. Homomorphic encryption eliminates the need for processing data in the clear, thereby preventing attacks that would enable a hacker to access that data while it is being processed, using privilege escalation. Homomorphic encryption is a form of encryption with an additional evaluation capability for computing over encrypted data without access to the secret key. Homomorphic encryption can be viewed as an extension of public-key cryptography. Homomorphic encryption includes multiple types of encryption schemes that can perform different classes of computations over encrypted data. The computations are represented as either Boolean or arithmetic circuits. Homomorphic encryption can be divided into different types of encryption, depending on how its designed. Some common types of homomorphic encryption are partially homomorphic, somewhat homomorphic, and fully homomorphic encryption. Fully homomorphic encryption is the holy grail of homomorphic encryption, as it allows an infinite number of additions or multiplications of ciphertexts while still producing a valid result. Homomorphic encryption is implemented so that its hidden from observers. Homomorphic encryption is used for securing data stored in the cloud, enabling data analytics in regulated industries, and sharing data sets with other companies[[5]](https://www.internetsociety.org/resources/doc/2023/homomorphic-enc...