Exploring the mathematics behind HE
The mathematics behind HE is based on two main concepts: encryption and homomorphism.
Encryption
Encryption is the process of transforming plaintext into ciphertext using an encryption algorithm and a secret key. The ciphertext can then be transmitted over a network or stored in a database without fear of unauthorized access. To decrypt the ciphertext and obtain the plaintext, the recipient must possess the secret key that was used to encrypt the data.
Homomorphism
Homomorphism is a mathematical property that allows an operation to be performed on ciphertexts, generating a new ciphertext that is the result of the operation on the plaintexts. This means that if we have two plaintexts x and y, and their respective ciphertexts C(x) and C(y), we can perform an operation on C(x) and C(y) to obtain a new ciphertext C(x+y), which can be decrypted to obtain the result of the operation on x and y.
The most commonly used homomorphic operations...