Design of McEliece Cryptosystem Based on QC-MDPC Codes

Abstract

The McEliece public key cryptosystem based on QC-MDPC codes has been shown to be a relatively secure system. McEliece cryptosystem has been shown to quantum resistant, which is faster and simpler compared with RSA. When different types of codes are used, most of the ciphers are easy to be cracked. Initially, the keys were all large matrices. For example, the size of the generating matrix of Goppa codes is 1024×524, and it increases exponentially with the increase of the coding length and the number of generated polynomials. In this paper, we use QC-MDPC codes instead of Goppa codes to reduce the key sizes and improve the decoding algorithm, which can resist all kinds of attacks. In the 5G era of the Internet of things, the application of this cryptosystem can guarantee more access security.