Deterministic public key encryption (D-PKE) provides an alternative to randomized public key encryption in various scenarios (e.g. search on encrypted data) where the latter exhibits inherent drawbacks. In CRYPTO\'11, Brakerski and Segev formalized a framework for studying the security of deterministic public key encryption schemes with respect to auxiliary inputs. A trivial requirement is that the plaintext should not be efficiently recoverable from the auxiliary inputs.
In this paper, we present an efficient deterministic public key encryption scheme in the auxiliary-input setting from lattices. The public key size, ciphertext size and ciphertext expansion factor are improved compared with the scheme proposed by Brakerski and Segev. Our scheme is also secure even in the multi-user setting where related messages may be encrypted under multiple public keys. In addition, the security of our scheme is based on the hardness of the learning with errors (LWE) problem which remains hard even for quantum algorithms.
Furthermore, we consider deterministic identity-based public key encryption (D-IBE) in the auxiliary-input setting.
The only known D-IBE scheme (without considering auxiliary inputs) in the standard model was proposed by Bellare et al. in EUROCRYPT\'12. However, this scheme is only secure in the selective security setting, and Bellare et al. identified it as an open problem to construct adaptively secure D-IBE schemes. The second contribution of this work is to propose a D-IBE scheme from lattices that is adaptively secure.