Complexity and performance of QC-MDPC code-based McEliece cryptosystems

In this paper, we analyze security of McEliece cryptosystem based on Low Density Parity Check (LDPC) and Moderate (MDPC) codes, as well as the complexity of the corresponding cryptosystem. Several approaches are proposed to improve the cryptosystem security for the case when complexity of cryptosystem has to be below the prescribed level. A certain modifications of Gradient Descent Bit Flipping (GDBF) decoding algorithm are identified as the crucial part of the cryptosystem that could provide a good trade-off between the complexity cost, decryption latency and security level.