A Study on the Security of Privacy Homomorphism

Informally, privacy homomorphism (PH) refers to encryption schemes with a homomorphic property allowing to obtain E_k(a + b) or E _k(a times b) from ciphertexts E_k(a) and E_k (b) without the knowledge of the decryption key. PH has a wide range of applications in information security due to its homomorphic property, but the best achievable security of them is yet unknown. In this paper, we discuss the security of PH in the black-box model and find that any PH is at most semantically secure under non-adaptive chosen-ciphertext attacks (i.e. IND-CCAI secure). We also show that the IND-CCAI security can be achieved with a small amount of hardware, namely, we offer a hardware-based solution to construct PH with provable security