A code-based hybrid signcryption scheme

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 a 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 NP-completeness of the equivalent subcode problem 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 an asymmetric- as well as a 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).