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

TL;DR

This paper introduces a memory-efficient layered decoding algorithm for BIKE's new bit-flipping decoder, reducing complexity and code length requirements for post-quantum cryptography.

Contribution

It proposes a layered decoder architecture for BIKE's BF algorithm, optimizing threshold coefficients and analyzing finite precision effects, achieving significant complexity reduction.

Findings

20% complexity reduction over prior methods

Reduced memory requirements for the decoder

Effective threshold coefficient optimization

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.