Modern variations of McEliece and Niederreiter cryptosystems

Classical cryptosystems proposed by Robert McEliece (1978) and Harold Niederreiter (1986) and their modern variations are studied. A detailed review of five code-based public key cryptosystems has been presented. It is shown that some of the modern interpretations of the classical McEliece and Niederreiter cryptosystems have significant issues. In particular, it has been established that the XGRS cryptosystem based on extended Reed-Solomon codes does not provide the declared level of security against the information set decoding attack, and also has a number of inaccuracies. It is shown that the time of key generation and decryption in modern cryptosystems is quite large, and the public and private keys take up a large amount of memory. The inaccuracies of the considered schemes revealed in this work can be used to improve and adjust the systems, as well as to build a more accurate assessment of their security level and efficiency. The presented cryptosystems can be considered as standards for post-quantum cryptography and can be used to protect data after development of powerful quantum computers.