Homomorphic Encryption

Abstract

Homomorphic Encryption is a class of encryption methods envisioned by Rivest, Adleman, and Dertouzos already in 1978, and first constructed by Craig Gentry in 2009. It differs from typical encryption methods in the sense that it allows computation operations to be performed directly on encrypted data without requiring access to a secret key (A Few Thoughts on Cryptographic Engineering). The result of such a computation remains in encrypted form, and can at a later point be revealed by the owner of the secret key. This form of encryption allows computation on ciphertexts, generating an encrypted result which, when decrypted, matches the result of the operations as if they had been performed on the plaintext. The purpose of Homomorphic Encryption is to allow computation on encrypted data. Usually, it is used for large-scale statistical analysis and mostly used in data encryption and decryption. Thus, it is used programs that rely mainly on information security and high-security documents in many governmental segments. The challenging aspect is performing statistical analysis on encrypted data and getting an accurate result, without putting the data through the risk of being stolen or having a backdoor copy for it.