RKA-secure public key encryptions against efficiently invertible functions

Related-key attacks (RKAs) are a flavor of powerful physical attacks, which allow an adversary to modify the secret key stored in a cryptographic device and subsequently observe the effect of such modifications on the output of the device. Designing secure encryption schemes against such attacks is a challenging task, especially for a large class of such physical attacks which are usually captured by related-key derivation functions. In this work, we achieve the security of public key encryptions (PKEs) against a new and broad function class that consists of almost all efficiently invertible functions in two different ways. Specifically, we first give a generic construction of PKE which is proven secure against such a broad function class under the standard chosen-ciphertext security. Moreover, we present two practical concrete constructions, both of which are shown to be secure against such function class under standard assumptions in the standard model. At last, we give a detailed performance analysis, which shows that our constructions can not only resist to a large class of RKAs but also achieve a good efficiency.