  Due to the weakness of public key cryptosystems encounter of quantum
computers, the need to provide a solution was emerged. The McEliece
cryptosystem and its security equivalent, the Niederreiter cryptosystem, which
are based on Goppa codes, are one of the solutions, but they are not practical
due to their long key length. Several prior attempts to decrease the length of
the public key in code-based cryptosystems involved substituting the Goppa code
family with other code families. However, these efforts ultimately proved to be
insecure. In 2016, the National Institute of Standards and Technology (NIST)
called for proposals from around the world to standardize post-quantum
cryptography (PQC) schemes to solve this issue. After receiving of various
proposals in this field, the Classic McEliece cryptosystem, as well as the
Hamming Quasi-Cyclic (HQC) and Bit Flipping Key Encapsulation (BIKE), chosen as
code-based encryption category cryptosystems that successfully progressed to
the final stage. This article proposes a method for developing a code-based
public key cryptography scheme that is both simple and implementable. The
proposed scheme has a much shorter public key length compared to the NIST
finalist cryptosystems. The key length for the primary parameters of the
McEliece cryptosystem (n=1024, k=524, t=50) ranges from 18 to 500 bits. The
security of this system is at least as strong as the security of the
Niederreiter cryptosystem. The proposed structure is based on the Niederreiter
cryptosystem which exhibits a set of highly advantageous properties that make
it a suitable candidate for implementation in all extant systems.
