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Privacy-Preserving Machine Learning
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The mathematics behind HE is based on two main concepts: encryption and homomorphism.
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 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...