Decoding of Generalized Concatenated Codes Over the One-Lee Error Channel for the McEliece Cryptosystem
Johann-Philipp Thiers, Jürgen Freudenberger · 2022 IEEE International Symposium on Information Theory (ISIT) · 2022
The code-based McEliece cryptosystem is a promising candidate for post-quantum cryptography. The sender encodes a message, using a public scrambled generator matrix, and adds a random error vector. In this work, we consider q-ary codes and restrict the Lee weight of the added error symbols. This leads to an increased error correction capability and a larger work factor for information-set decoding attacks. In particular, we consider codes over an extension field and use the one-Lee error channel, which restricts the error values to Lee weight one. For this channel model, generalized concatenated codes can achieve high error correction capabilities. We discuss the decoding of those codes and the possible gain for decoding beyond the guaranteed error correction capability.