In [1], Bellare, Boldyreva, and Micali addressed the security of public-key encryptions (PKEs) in a multi-user setting (called the BBM model in this paper). They showed that although the indistinguishability in the BBM model is induced from that in the conventional model, its reduction is far from tight in general, and this brings a serious key length problem. In this paper, we discuss PKE schemes in which the IND-CCA security in the BBM model can be obtained tightly from the IND-CCA security. We call such PKE schemes IND-CCA secure in the BBM model with invariant security reductions (briefly, SR-invariant IND-CCA^BBM secure). These schemes never suffer from the underlying key length problem in the BBM model. We present three instances of an SR-invariant IND-CCA^BBM secure PKE scheme: the first is based on the Fujisaki-Okamoto PKE scheme [7], the second is based on the Bellare-Rogaway PKE scheme [3], and the last is based on the Cramer-Shoup PKE scheme [5].