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

PKC-PC: A Variant of the McEliece Public Key Cryptosystem based on Polar Codes