What type of encryption allows operations on ciphertext without decryption?

Homomorphic encryption is a special type of encryption that uniquely allows computations to be performed on ciphertexts, generating an encrypted result that, when decrypted, matches the result of operations performed on the plaintext. This property is significant because it enables users to process data securely without exposing the underlying plaintext data to untrusted environments or parties.

For example, with homomorphic encryption, a cloud service can process sensitive financial data for a client without ever accessing the actual data. This capability is particularly valuable in scenarios where privacy is paramount, such as healthcare and finance, as it supports secure data analysis and calculations while maintaining confidentiality.

In contrast, symmetric encryption involves using the same key for both encryption and decryption, requiring data to be decrypted before any operations can be conducted, which does not allow for computations on ciphertext. Elliptic curve encryption is a form of asymmetric encryption that provides security through mathematical properties of elliptic curves but also requires decryption for operations. Hashing algorithms, while useful for data integrity verification, are not encryption techniques and do not enable encrypted computations.