*4.1. Algebraic Attack*

The security of a public-key cryptosystem depends on the security of the private-key. So, the first attack will be factorization *H* to find the private-keys *G*, *H*, and *M*. If the code parameters *n*, *k*, *d* are large enough, this attack is impracticable, because it is difficult to recover the factors of *H* . This means the security is ensured with the private-key. The security of the new system is also based on decoding in the code *H* , while *H* is not only non-equivalent to the code *H* in the cryptosystem, but after multiplying *H<sup>T</sup>* by *M* from the right, the error-correction capability of public-key *H* is unknown. Furthermore, the vector *h* is secret. Thus, the best attack may not carry out the complete decoding.
