**5. Comparison with the Other Public-Key Cryptosystems**

In this section, we compare our system with the other code-based cryptosystem for an [*n*, *<sup>k</sup>*, *<sup>d</sup>*]-code *<sup>C</sup>* over <sup>F</sup>*q*, where *<sup>d</sup>* <sup>≥</sup> <sup>2</sup>*<sup>t</sup>* <sup>+</sup> 1. We denote by *<sup>S</sup>*, *<sup>R</sup>*, *<sup>T</sup>*, and *<sup>K</sup>*, respectively, the size of plaintext, ciphertext, the transmission rate, and the dimension of the public-key.

The new system is a further development of the McEliece and Niederreiter cryptosystems. McEliece's system is constructed based on binary linear codes, but both Niederreiter's and our new system are constructed based on linear codes over F*q*. Especially, we use the bounded distance decoding to construct our system. In the new system, as the public-key is smaller than McEliece's cryptosystem, it is more useful in industry. Moreover, as it is seen in Table 1, the plaintext is a word of small weight, which is one of the coset leaders, and the number of operations involved during the encryption is less than McEliece's cryptosystem. Furthermore, it is seen that the public-keys in our system and Niederreiter's system are equivalent. However, our system is more effective than Niederreiter's cryptosystem, since it is easier to generate the pieces of keys. This condition increases the security. It is impossible to reach the private-key with public-key by an attacker in the new system. In addition, the plaintext cannot be calculated even if the public-key and ciphertext are known by an enemy cryptanalyst. When the transmission rates of systems are compared, it is noticed that the proposed system has the bigger magnitude. That is, the encryption is faster than the others. So, it is more reliable by means of security.


**Table 1.** Comparison with other schemes.
