# Recurrent Bipartite Graph Neural Networks for QC-MDPC Error Decoding in McEliece Cryptosystems

DevFeed: [Recurrent Bipartite Graph Neural Networks for QC-MDPC Error Decoding in McEliece Cryptosystems](<https://devfeed.tech/articles/recurrent-bipartite-graph-neural-networks-for-qc-mdpc-error-decoding-in-mceliece-cryptosystems-108693.md>)

Original publisher: [Read original article](<https://arxiv.org/abs/2610.38479>)

Author: Parth Rajeshkumar Tandel, Elisabeth Fink

Published: 2026-10-30T04:00:00Z

Content type: article

Language: en

Sources: [arXiv: Cryptography and Security](<https://devfeed.tech/sources/arxiv-cryptography-and-security.md>), [arXiv: Machine Learning](<https://devfeed.tech/sources/arxiv-machine-learning.md>)

Topics: [Post-quantum cryptography](<https://devfeed.tech/topics/post-quantum-cryptography.md>), [Cryptography](<https://devfeed.tech/topics/cryptography.md>), [Neural Network](<https://devfeed.tech/topics/neural-network.md>), [Decoding](<https://devfeed.tech/topics/decoding.md>), [graph theory](<https://devfeed.tech/topics/graph-theory.md>)

Tags: [algorithms](<https://devfeed.tech/tags/algorithms.md>), [cryptography](<https://devfeed.tech/tags/cryptography.md>), [cs-cr](<https://devfeed.tech/tags/cs-cr.md>), [cs-lg](<https://devfeed.tech/tags/cs-lg.md>), [cycles](<https://devfeed.tech/tags/cycles.md>), [decoder](<https://devfeed.tech/tags/decoder.md>), [decoding](<https://devfeed.tech/tags/decoding.md>), [encryption](<https://devfeed.tech/tags/encryption.md>), [error](<https://devfeed.tech/tags/error.md>), [failure](<https://devfeed.tech/tags/failure.md>), [graph](<https://devfeed.tech/tags/graph.md>), [graph-neural-networks](<https://devfeed.tech/tags/graph-neural-networks.md>), [key](<https://devfeed.tech/tags/key.md>), [leak](<https://devfeed.tech/tags/leak.md>), [network](<https://devfeed.tech/tags/network.md>), [neural](<https://devfeed.tech/tags/neural.md>), [noise](<https://devfeed.tech/tags/noise.md>), [post-quantum](<https://devfeed.tech/tags/post-quantum.md>), [post-quantum-cryptography](<https://devfeed.tech/tags/post-quantum-cryptography.md>), [post-quantum-cryptography-pqc](<https://devfeed.tech/tags/post-quantum-cryptography-pqc.md>), [qc](<https://devfeed.tech/tags/qc.md>), [recurrent](<https://devfeed.tech/tags/recurrent.md>)

## AI overview

The paper proposes a recurrent bipartite graph neural network (R-BGNN) for decoding QC-MDPC codes in McEliece cryptosystems. It incorporates Gated Recurrent Units into message passing and uses multi-topology curriculum training to learn to break limit-cycle oscillations that can stall decoding. On 20 unseen matrix topologies, the abstract reports that it outperforms Bit-Flipping and Min-Sum baselines, with a 63.7% lower decoding failure rate at moderate noise (t=10) and convergence in fewer iterations. The supplied abstract describes this as a proof of concept.

## Source excerpt

arXiv:2610.38479v1 Announce Type: cross Abstract: As the advent of large-scale quantum computing threatens classical encryption, Quasi-Cyclic Moderate Density Parity-Check (QC-MDPC) codes have emerged as a foundational element of Post-Quantum Cryptography (PQC). However, decoding these relatively dense codes using classical Belief Propagation algorithms often leads to failures caused by short graph cycles that stall the decoder. In cryptographic applications, these failures are severe security vulnerabilities that leak secret key information. To address this, this paper proposes a Recurrent Bipartite Graph Neural Network (R-BGNN) as proof of concept. By integrating Gated Recurrent Units (GRUs) into the message-passing framework and employing a multi-topology curriculum training strategy, the R-BGNN actively learns to break limit-cycle oscillations. Evaluated across 20 unseen matrix topologies, the proposed architecture significantly outperforms classical Bit-Flipping and Min-Sum baselines, reducing the Decoding Failure Rate (DFR) by 63.7\% at moderate noise levels ($t=10$) while converging in fewer iterations.