Cryptosystem based on induced group codes

The code $C$ on a group $\mathcal{G}$, induced by the code $N$ on a subgroup $\mathcal{H}$, has the property that for decoding the code $C$ one can use the decoder for the code $N$. Therefore, if $N$ has an efficient algorithm for decoding, we can build a class of induced codes with known decoding algorithms. This feature is used in this paper to build the code McEliece-type public key cryptosystems on induced group codes. For this cryptosystem we described operations of encryption and decryption, an analysis of the resistance to the attack on the private key is proposed, and also weak keys are highlighted, which is used while breaking McEliece-type cryptosystem on the induced code $C$ is reduced to breaking this cryptosystem on the code $N$. It is shown that a practically resistant cryptosystem on the induced code $C$ can be built on the code $N$ with small length. Based on the proposed cryptosystem a common protocol for open channel key generation is developed.