Punctured Reed-Muller code-based McEliece cryptosystems

The authors propose new McEliece cryptosystems based on punctured Reed–Muller (RM) codes. They successfully show that the commonly known attacks, such as the Minder–Shokrollahi attack, the Chizhov–Borodin attack, and the square code attack, are ineffective against the proposed RM code-based McEliece cryptosystem. We developed an optimal puncturing scheme to prevent the above-mentioned attacks for the proposed RM code-based cryptosystems in a sense that the exact locations of puncturing positions with the minimum number of punctured columns of the generator matrix should be found for attacking. It is important to carry out the minimum number of punctures, however, as code modification resulting from puncturing can reduce security. Additionally, the square code attack can be prevented in the proposed RM code-based McEliece cryptosystems by using both the proposed puncturing method and random insertion methods.