Homomorphic encryption is a cryptographic primitive defined by an evaluation algorithm capable of computing functions on ciphertexts such that decryption yields the result equivalent to applying the function on plaintext, without requiring access to private keys. The core theoretical mechanism relies on constructing schemes where efficiency and correctness are maintained asymptotically within polynomial time bounds for specific function classes (e.g., XOR or additive operations), distinguishing between symmetric cases utilizing empty evaluation keys and asymmetric cases using public components derived from key generation algorithms. This concept extends the parent discipline of cryptography by addressing computational privacy constraints, specifically enabling ind-CPA secure environments that support computation on encrypted data while exploring trade-offs regarding full homomorphism capabilities versus functional security properties like function hiding under non-trivial complexity assumptions.
Homomorphic encryption is a cryptographic primitive defined by an evaluation algorithm capable of computing functions on ciphertexts such that decryption yields the result equivalent to applying the …