The support splitting algorithm for induced codes

In the paper, the analysis of the stability of the McEliece-type cryptosystem on induced codes for key attacks is examined. In particular, a model is considered when the automorphism group is trivial for the base code $C$, on the basis of which the induced code $ \mathbb{F}^l_q \otimes C $ is constructed. In this case, as shown by N. Sendrier in 2000, there exists such a mapping, called a complete discriminant, by means of which a secret permutation that is part of the secret key of a McEliece-type cryptosystem can be effectively found. The automorphism group of the code $ \mathbb{F}^l_q \otimes C $ is nontrivial, therefore there is no complete discriminant for this code. This suggests a potentially high resistance of the McEliece-type cryptosystem on the code $ \mathbb{F}^l_q \otimes C $. The algorithm for splitting the support for the code $ \mathbb{F}^l_q \otimes C $ is constructed and the efficiency of this algorithm is compared with the existing attack on the key of the McElice type cryptosystem based on the code $ \mathbb{F}^l_q \otimes C $.