Improved encryption schemes based on McEliece scheme using polar codes

In this paper, we design two public key encryption schemes based on polar codes. Firstly, we propose a direct modification of the McEliece scheme. We use the added error vector to carry additional information bits. Theoretically, the rate of this scheme can be increased to one bit/channel use. However, due to carrying more information, the security of the system is less guaranteed. To address this issue, we propose a new variant of the McEliece scheme, which replaces the "XOR" operation between the codeword and the noise vector with addition in the real number filed, i.e., a two-user binary erasure-multiple access channel (BE-MAC) is formed in the encryption. During the research on BE-MAC, we propose a construction method to enhance the decoding performance. To validate the security and efficiency of these encryption systems, we conduct numerous experiments and simulations. The results demonstrate that scheme 2 has good performance in terms of both safety and efficiency.