Evolution of the McEliece Public Key Encryption Scheme

The evolution of the McEliece encryption scheme is a long and thrilling research process. The code families supposed to securely reduce the key size of the original scheme were often cryptanalyzed and thus the future of the code-based cryptography was many times doubted. Yet from this long evolution emerged a great comprehension and understanding of the main difficulties and advantages that coding theory can offer to the field of public key cryptography. Nowadays codebased cryptography has become one of the most promising solutions to post-quantum cryptography. We analyze in this article the evolution of the main encryption variants coming from this field. We stress out the main security issues and point out some new ideas coming from the Rank based cryptography. A summary of the remaining secure variants is given in Fig. 2.