On the structural features of the key space of the McEliece–Sidelnikov cryptosystem based on generalized Reed–Solomon codes

The equivalence classes of secret keys of McEliece–Sidelnikov-type cryptosystems are investigated. We introduce the concept of codes with decomposable square and find relationships characterizing the equivalence classes in case when the cryptosystem is based on such codes. Some results for the specific case of using generalized Reed-Solomon codes are refined. Several examples of codes based on generalized Reed-Solomon codes with guaranteed indecomposable square are given.