  A key encapsulation mechanism (KEM) that takes as input an arbitrary string,
i.e., a tag, is known as tag-KEM, while a scheme that combines signature and
encryption is called signcryption. In this paper, we present a code-based
signcryption tag-KEM scheme. We utilize a code-based signature and an IND-CCA2
(adaptive chosen ciphertext attack) secure version of McEliece's encryption
scheme. The proposed scheme uses an equivalent subcode as a public code for the
receiver, making the NPcompleteness of the subcode equivalence problem to be
one of our main security assumptions. We then base the signcryption tag-KEM to
design a code-based hybrid signcryption scheme. A hybrid scheme deploys
asymmetric- as well as symmetric-key encryption. We give security analyses of
both our schemes in the standard model and prove that they are secure against
IND-CCA2 (indistinguishability under adaptive chosen ciphertext attack) and
SUF-CMA (strong existential unforgeability under chosen message attack).
