Completeness of Single-Bit Projection-KDM Security for Public Key Encryption

Abstract

Applebaum (EUROCRYPT 2011, J. Cryptology 2014) showed that it is possible to convert a public key encryption (PKE) scheme which is key dependent message (KDM) secure with respect to projection functions (also called projection-KDM secure) into a PKE scheme which is KDM secure with respect to any function family that can be computed in fixed polynomial time, without using any other assumption. This result holds in both of the chosen plaintext attack (CPA) and the chosen ciphertext attack (CCA) settings. In the CPA setting, he furthermore showed that even a projection-KDM secure 1-bit PKE scheme is sufficient to construct a KDM secure PKE scheme with respect to polynomial time computable functions. The existence of the latter trivially implies that of the former, and in this sense, he mentioned that single-bit projection-KDM security in the CPA setting and (multi-bit) projection-KDM security in the CCA setting are complete.