Three properties that a good homomorphic encryption should satisfy

A homomorphic encryption refers to the encryption of plaintext , It can be calculated according to ciphertext , then , The result of decryption is consistent with that of plaintext operation . In addition to the basic homomorphism requirements , A good homomorphic encryption scheme should satisfy the following three properties ： Semantic security 、 Compact and efficient decryption .

Semantic security or IND-CPA Security

Given two plaintext and , The corresponding homomorphic encrypted ciphertexts are and . Suppose the enemy only knows one of the ciphertexts c, The best he can do is The probability of judging c yes still , among Is a positive infinitesimal . in other words , The enemy cannot use any effective algorithm to judge c yes still , The best way is to guess randomly . It means , Ciphertext will not disclose any information of plaintext . Generally speaking , This is achieved by adding random factors in the encryption process .

compact

A homomorphic scheme is compact , It means that the size of the ciphertext will not increase with homomorphic calculation . in other words , The ciphertext obtained by homomorphic calculation should be as large as that obtained by directly encrypting the result . This ensures that multiple homomorphic calculations can be performed , It will not cause the expansion of ciphertext size . meanwhile , It also makes the ciphertext obtained by homomorphic calculation indistinguishable from the ciphertext directly encrypted , Better security .

Efficient decryption

Efficient decryption means , Decryption of a homomorphic scheme , The complexity of decryption will not be increased because the ciphertext is homomorphically calculated many times . in other words , Decryption does not depend on whether the ciphertext is homomorphically computed . This makes decryption independent of homomorphic computation .