Discrete algebra-based neural models for secure information transmission

Secure and reliable transmission over noisy and adversarial channels remains a critical challenge in modern communication systems. We introduce a discrete algebra–driven neural framework that embeds finite-field arithmetic directly into learned encoding and decoding layers, combining classical error-correcting code structures with trainable neural masks. Evaluated on both AWGN and real-world packet-loss traces, our hybrid model achieves bit-error rates below 10–4 at 6 dB SNR—a tenfold improvement over Hamming codes—while reducing information leakage by 30 % compared to a pure neural autoencoder. Despite these gains, end-to-end latency remains under 0.8 ms per 128-bit block on a Google Colab T4 GPU. These results demonstrate that discrete algebra–aware neural architectures can jointly optimize reconstruction fidelity and confidentiality, offering a practical path to robust, secrecy-preserving communications under realistic threat models. Our training employs a joint loss combining mean-squared reconstruction error with a mutual-information penalty to enforce secrecy and incorporates ℓ∞-bounded adversarial perturbations for robustness. The resulting model generalizes across dynamically varying noise and loss patterns, preserving algebraic invariants while adapting to channel impairments. This work highlights the potential of integrating discrete algebraic theory with deep learning to achieve high-assurance communication in the presence of sophisticated eavesdroppers.