We propose a generic method that transforms a weakly secure KEM, i.e. a KEM which is secure against constrained chosen ciphertext attack (CCCA), to a strongly secure KEM, i.e. a KEM which is secure against full chosen ciphertext attack (CCA). The proposed method does not depend on the random oracle nor any other non- standard assumptions. Using this method, we obtain new efficient hybrid encryption schemes based on Kurosawa&Desmedt and Hofheinz&Kiltz weakly secure KEMs. These are the first hybrid encryption schemes which are as efficient as Kurosawa&Desmedt and Hofheinz&Kiltz encryption schemes, but whose security can be explained in the original KEM/DEM framework.