Strong Converse Theorem for Source Encryption under Side-Channel Attacks

We are interested in investigating the security of source encryption with symmetric key under the side-channel attacks. In this paper, we propose a general model of source encryption with symmetric key under the side-channel attacks which can be apply to any kind of source encryption with symmetric key. We also propose a new security criterion for strong secrecy in the case of side-channel attacks which can be seen as a natural extension of the mutual information, i.e., \emph{the maximum conditional mutual information between the plaintext and the ciphertext given the adversarial key leakage, where the maximum is taken over all possible plaintext distribution}. Under this new criterion, we successfully formulate the rate region which serves as both necessary and sufficient conditions to have secure transmission even under side-channel attacks. Furthermore, we also prove another theoretical result regarding our new security criterion which might be interesting in its own right, i.e., although our new security criterion is clearly more strict compared to the standard security criterion which is the simple mutual information, in the case of discrete memoryless source, no perfect secrecy under standard security criterion can be achieved without achieving perfect secrecy in this new security criterion.