  We are interested in investigating the security of source encryption with a
symmetric key under side-channel attacks. In this paper, we propose a general
framework of source encryption with a symmetric key under the side-channel
attacks, which applies to \emph{any} source encryption with a symmetric key and
\emph{any} kind of side-channel attacks targeting the secret key. We also
propose a new security criterion for strong secrecy under side-channel attacks,
which is a natural extension of 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 on our new security criterion, which might be
interesting in its own right: in the case of the discrete memoryless source, no
perfect secrecy under side-channel attacks in the standard security criterion,
i.e., the ordinary mutual information, is achievable without achieving perfect
secrecy in this new security criterion, although our new security criterion is
more strict than the standard security criterion.
