Paper 2026/982

Zero-shot deep-unfolding decoder for QC-MDPC McEliece cryptosystems

Abstract

The QC-MDPC McEliece cryptosystem is a promising candidate for post-quantum cryptography, and the decoding performance of the underlying QC-MDPC code directly affects the security of the scheme. Deep unfolding, a framework that unfolds an iterative algorithm into a neural network with trainable weights, has been shown to improve belief propagation (BP) decoding for codes with dense parity-check matrices. However, applying deep unfolding directly to the large QC-MDPC codes used in practice is impractical owing to the computational cost of training. Moreover, in QC-MDPC-based cryptosystems, the parity-check matrix serves as the secret key and must be replaced periodically; key-specific training would therefore need to be repeated at each replacement. We address both issues through zero-shot transfer. We propose weight homogenisation, which constrains the trainable weights to a single scalar per iteration, making them independent of the specific Tanner graph. This enables a decoder trained on a small QC-MDPC code to be applied directly to larger codes. Experiments on QC-MDPC codes with parameters proposed for 80-bit and 128-bit security demonstrate that the proposed method achieves a lower decoding error rate than standard BP.