Approximate-Deterministic Public Key Encryption from Hard Learning Problems

We introduce the notion of approximate-deterministic public key encryption (A-DPKE), which extends the notion of deterministic public key encryption (DPKE) by allowing the encryption algorithm to be “slightly” randomized. However, a ciphertext convergence property is required for A-DPKE such that the ciphertexts of a message are gathering in a small metric space, while ciphertexts of different messages can be distinguished easily. Thus, A-DPKE maintains the convenience of DPKE in fast search and de-duplication on encrypted data, and encompasses new constructions. We present two simple constructions of A-DPKE, respectively from the learning parity with noise and the learning with errors assumptions.