McEliece-type cryptosystem based on correction of errors and erasures

Recently, a modification of the classical McEliece cryptosystem has been proposed by introducing an auxiliary matrix, by which an artificial error vector is multiplied. The system was broken. In this work, we propose a simpler attack on the system, and at the same time, we propose a generalization of the system, free from the identified shortcomings. We assume that the new scheme is at least as secure as McEliece’s cryptosystem.