Paper 2021/837 Original: eprint.iacr.org/2021/837 ↗

On McEliece type cryptosystems using self-dual codes with large minimum weight

Abstract

One of the finalists in the NIST post-quantum cryptography competition is the Classic McEliece cryptosystem. Unfortunately, its public key size represents a practical limitation. One option to address this problem is to use different families of error-correcting codes. Most of such attempts failed as those cryptosystems were proved not secure. In this paper, we propose a McEliece type cryptosystem using high minimum distance self-dual codes and punctured codes derived from them. To the best of our knowledge, such codes have not been implemented in a code-based cryptosystem until now. For the 80-bit security case, we construct an optimal self-dual code of length 1\,064, which, as far as we are aware, was not presented before. Compared to the original McEliece cryptosystem, this allows us to reduce the key size by about 38.5\%.