Efficient Layered New Bit-Flipping QC-MDPC Decoder for BIKE Post-Quantum Cryptography

TL;DR

This work tackles the memory bottleneck in BIKE's MDPC-based post-quantum cryptography by introducing a column-layered BIKE BF decoder that updates syndromes in place, eliminating the need to store multiple iteration states. It simultaneously optimizes the affine BF-threshold function and analyzes the impact of finite-precision representations on decoding performance, identifying precision-robust configurations (e.g., seven-bit precision) and giving explicit optimal coefficients for 128-bit security. The approach yields approximately a 20% reduction in hardware complexity with only a modest latency increase for a representative MDPC code at $\lambda=128$, and demonstrates substantial memory savings via a layered, parallel architecture. These results support more practical, hardware-friendly BIKE implementations suitable for standardization and deployment in post-quantum cryptographic systems.

Abstract

The medium-density parity-check (MDPC) code-based Bit Flipping Key Encapsulation (BIKE) mechanism remains a candidate of post-quantum cryptography standardization. The latest version utilizes a new bit-flipping (BF) decoding algorithm, which decides the BF threshold by an affine function with high-precision coefficients. Previous BF decoder implementations can be extended to the new algorithm. However, they suffer from large memories that dominate the overall complexity. This paper proposes a column-layered decoder for the new BIKE BF decoding algorithm to substantially reduce the memory requirement, and optimizes the affine BF threshold function coefficients to reduce the code length needed for the same security level. For the first time, our work also investigates the impact of finite precision representation of the threshold coefficients on the decoding performance. For an example MDPC code considered for the standard, the proposed layered BF decoder achieves 20% complexity reduction compared to the best prior effort with a very small latency overhead.

Figures (4)

• Figure 1: DFRs of the new BIKE BF decoder with different threshold coefficients and the extrapolation of $r$ required by $\lambda=128$ for MDPC codes with $(w, t)=(142,134)$ and $I_{\text{max}}=7$.
• Figure 2: DFRs of optimal non-layered decoder and layered decoders with different $a$ and $b$ values for MDPC codes with $(\lambda, w, t)=(128, 142,134)$ and $I_{\text{max}}=7$.
• Figure 3: DFRs of parallel layered BF decoder with different precision in $a$ and $b$ for MDPC codes with $(\lambda, w, t)=(128, 142,134)$, $L$=32, and $I_{\text{max}}=7$.
• Figure 4: Top-level block diagram of the proposed layered new BF decoder.