Abstract: In terms of F-metric, the maximum F-distance code was constructed, a new modification of the McEhece publie key cryptosystem based on maximum F-distance codes was proposed. The legal party chooses a random matrix as an extra secret key and adds it to the original public key to produce a new modified public key. It makes such cryptosystem effective for resisting the attack based on getting private keys from known public keys. Moreover, using F-metric increases the complexity of the system, making it harder to attack allowing for smaller key sizes. Attacks on such a system were also investigated. It is shown that the McEliece public key cryptosystem based on maximum F-distance codes is security and feasibility.

Key words: F-metric, Maximum F-distance code, New McElicce public key cryptosystem, Security