  Polar codes are novel and efficient error correcting codes with low encoding
and decoding complexities. These codes have a channel dependent generator
matrix which is determined by the code dimension, code length and transmission
channel parameters. This paper studies a variant of the McEliece public key
cryptosystem based on polar codes, called "PKC-PC". Due to the fact that the
structure of polar codes' generator matrix depends on the parameters of
channel, we used an efficient approach to conceal their generator matrix. Then,
by the help of the characteristics of polar codes and also introducing an
efficient approach, we reduced the public and private key sizes of the PKC-PC
and increased its information rate compared to the McEliece cryptosystem. It
was shown that polar codes are able to yield an increased security level
against conventional attacks and possible vulnerabilities on the code-based
public key cryptosystems. Moreover, it is indicated that the security of the
PKC-PC is reduced to solve NP-complete problems. Compared to other post-quantum
public key schemes, we believe that the PKC-PC is a promising candidate for
NIST post-quantum crypto standardization.
