Homomorphic Encryption

Definition

Homomorphic encryption is a form of public-key encryption where one can perform a specific algebraic operation on the plaintext by performing an (possibly different) algebraic operation on the ciphertext. For example, knowing only C₁ = (x) and C₂ = (y), but not x, y, one may be able to get (x + y) by calculating C₁ × C₂. A homomorphic encryption scheme allows a third party to operate on encrypted values without knowing the plaintext.

Key Points

Depending on the intended application, the homomorphic property can be seen as a positive or negative attribute of the cryptosystem. Homomorphic encryption schemes are malleable by design. On the other hand, the ability to enable manipulating ciphertexts without being able to decrypt can be very useful in some applications.

A fully homomorphic encryption scheme enables one to perform operations on the ciphertext to achieve both addition and multiplication on the enclosed plaintext. This enables one to compute arbitrary functions on...