Chosen Ciphertext Secure Keyed Two-Level Homomorphic Encryption

Homomorphic encryption (HE) is a useful variant of public key encryption (PKE), but it has a drawback that HE cannot fully achieve IND-CCA2 security, a standard security notion for PKE. Emura et al. (PKC 2013) proposed a "keyed" version of HE, called KH-PKE, which introduces a separate key for homomorphic evaluation and then achieves security close to IND-CCA2. Current KH-PKE schemes are classified into ones supporting only a single kind of homomorphic operation (addition or multiplication) and others that are fully homomorphic but are consequently not very efficient; no intermediate schemes with both efficiency and richer functionality are known so far. In this paper, we propose a "two-level" KH-PKE scheme for evaluating degree-two polynomials, by cleverly combining Emura et al.'s generic framework with a recent efficient two-level HE by Attrapadung et al. (ASIACCS 2018).