Analyzing the Impact of Thresholds in Bit-Flipping Decoding for QC-MDPC based McEliece cryptosystems

This paper investigates the effect of various threshold configurations in the bit-flipping decoding algorithm for quasi-cyclic moderate density parity-check (QC-MDPC) codes within the McEliece cryptosystem. The choice of threshold plays a crucial role in determining the efficiency and accuracy of error correction in these code-based cryptographic schemes. We propose and evaluate several threshold formulas, comparing their performance across different error weights and security levels. Our results highlight the impact of threshold adjustments on the average number of decoding iterations, decoding failure rates (DFR), and syndrome weight behavior over multiple iterations. Through extensive simulations, we demonstrate how optimal threshold selection can significantly enhance the decoding process, providing insights for improving the robustness of postquantum secure McEliece cryptosystems.