We propose a generic way for deriving an identification (ID) scheme secure against concurrent man-in-the-middle attacks from a key encapsulation mechanism (KEM) secure against chosen ciphertext attacks on one-wayness (oneway-CCA). Then we give a concrete one-way-CCA secure KEM based on the Computational Diffie-Hellman (CDH) assumption. In that construction, the Twin Diffie-Hellman technique of Cash, Kiltz and Shoup is essentially employed. We compare efficiency of the ID scheme derived from our KEM with previously known ID schemes and KEMs. It turns out that our KEM-based ID scheme reduces the computation by one exponentiation than the currently most efficient one derived from the Hanaoka-Kurosawa one-way-CCA secure KEM, whose security is based on the same (CDH) assumption.