AbstractThis is a survey on the theory of skew‐cyclic codes over the ring , where v2 = v. Coding theory plays an important role in the constructing cryptosystems. In this survey, we propose a public‐key cryptosystem using skew‐cyclic codes. The encryption is done by the Gray map ψ and the projection map φ is used for decryption. This approach is different from the others. More importantly, it is a secure system.