Generalized Concatenated Codes over Gaussian and Eisenstein Integers for Code-Based Cryptography

The code-based McEliece and Niederreiter cryptosystems are promising candidates for post-quantum public-key encryption. Recently, q-ary concatenated codes over Gaussian integers were proposed the cryptosystem, together with one-Mannheim error channel, where values limited to Mannheim weight one. Due values, achieve a higher correction capability than maximum distance separable (MDS) bounded minimum decoding. This improves work factor regarding decoding attacks based on information-set also enable low complexity algorithm beyond guaranteed capability. In this work, we extend coding scheme Eisenstein integers. These have advantages system. Additionally, propose an improved code construction generalized codes. rate region, is beneficial compared MDS Moreover, more robust against structural ordinary