In this paper, we show that a key encapsulation mechanism (KEM) does not have to be IND-CCA secure in the construction of hybrid encryption schemes, as was previously believed. That is, we present a more efficient hybrid encryption scheme than Shoup [12] by using a KEM which is not necessarily IND-CCA secure. Nevertheless, our scheme is secure in the sense of IND-CCA under the DDH assumption in the standard model. This result is further generalized to universal2 projective hash families.