Expanded low-rank parity-check codes and their application to cryptography

Abstract

In this paper, we define expanded LRPC codes from LRPC codes with a decoding algorithm using the one of the underlying LRPC codes. Next, we propose to use these codes for cryptography by deriving two cryptosystems in a McEliece setting. in order to reduce the key sizes, we use a generator matrix in systematic form for the first scheme, and an m − order quasi-cyclic LRPC code that we define for the second scheme. The obtained code has a very poor structure and is more likely to be a random linear code. Next, we give some security parameters and compare the key sizes of our public key with the key sizes of some cryptosystems.