Efficient KDM-CCA Secure Public-Key Encryption via Auxiliary-Input Authenticated Encryption. (11th December 2017) - Han, Shuai; Liu, Shengli; Lyu, Lin
Abstract : KDM[ F ] -CCA security of public-key encryption (PKE) ensures the privacy of key-dependent messages f ( s k ) which are closely related to the secret key s k, where f ∈ F, even if the adversary is allowed to make decryption queries. In this paper, we study the design of KDM-CCA secure PKE. To this end, we develop a new primitive named Auxiliary-Input Authenticated Encryption (AIAE ). For AIAE, we introduce two related-key attack (RKA) security notions, including IND-RKA and weak-INT-RKA . We present a generic construction of AIAE from tag-based hash proof system (HPS) and one-time secure authenticated encryption (AE) and give an instantiation of AIAE under the Decisional Diffie-Hellman (DDH) assumption. Using AIAE as an essential building block, we give two constructions of efficient KDM-CCA secure PKE based on the DDH and the Decisional Composite Residuosity (DCR) assumptions. Specifically, (i) our first PKE construction is the first one achieving KDM[ F a f f ] -CCA security for the set of affine functions and compactness of ciphertexts simultaneously. (ii) Our second PKE construction is the first one achieving KDM[ F p o l y d ] -CCA security for the set of polynomial functions and almost compactness of ciphertexts simultaneously. Our PKE constructions are very efficient; in particular, they are pairing-free and NIZK-free.