Learning the Word Problem: Geodesic Lengths and Cryptographic Applications

The Word Problem has been a subject of intensive mathematical study for over a century, initially driving advances in combinatorial group theory and more recently emerging as a foundational hardness assumption in post-quantum cryptography (PQC). While generally undecidable, several families of infinite non-abelian groups exhibit solvable or algorithmically fast word problems, making them attractive platforms for cryptographic design. This paper introduces WPNet, a novel Graph Neural Network architecture capable of solving the Word Problem heuristically, which is demonstrated on the Baumslag-Solitar group $BS(1,2)$ and on an Artin group. By mapping unreduced words to dynamic graph structures, the model learns to cluster algebraically equivalent elements in a continuous embedding space, effectively identifying the geodesic representative of a word without executing discrete reduction steps. As an application, a model variant is developed that can predict the geodesic length of an unreduced word in both groups. To demonstrate the cryptographic severity of this structural leakage, WPNet is successfully deployed against the Wagner-Magyarik public-key cryptosystem.

Towards quantum machine learning for assessing the resilience of post-quantum cryptography

The potential capabilities of quantum computers motivated the development of cryptographic protocols suitable for securing communication against adversaries with access to large fault-tolerant quantum computers. However, even though current quantum computers are limited in terms of size and precision, they can still be useful for finding loopholes and weaknesses in the post-quantum cryptographic protocols. In this work, we present an attempt to utilize the capabilities of Quantum Generative Adversarial Networks (QGANs), one of the promising architectures used in quantum machine learning, for this purpose. We describe an example application of QGAN architecture for the purpose of loading the probability distribution of the hash-based digital signatures into the memory of a quantum computer. Our results confirm that near-term hybrid quantum-classical methods possess capabilities required for this purpose. The presented approach can be used as a first step in the workflow, enabling the utilization of quantum computing for attacking post-quantum cryptographic primitives.

Secure Coding Drift in LLM-Assisted Post-Quantum Cryptography Development: A Gamified Fix

The transition to Post Quantum Cryptography (PQC) introduces considerable implementation complexity, requiring strict adherence to constant-time execution, side channel resistance, and precise parametrisation. Simultaneously, large language models (LLMs) are heavily embedded in software development workflows, including cryptographic engineering. While LLMs improve productivity, evidence shows that they frequently generate insecure or suboptimal code, particularly in security critical domains. This paper introduces Secure Coding Drift in PQC, a novel socio technical vulnerability model capturing the gradual degradation of secure coding practices due to sustained reliance on LLM-generated code. Unlike prior work that focuses on static vulnerabilities, we conceptualise security risk as a longitudinal behavioural phenomenon rising from human AI interaction. To mitigate this, we propose a gamified, LLM augmented secure coding framework that embeds adversarial evaluation, behavioural feedback, and security scoring into development workflows. Our approach reframes LLMs from passive assistants into active security co-pilots, contributing toward safer PQC implementation in AI mediated environments.

Securing the Future of IoMT in the Post-Quantum Era: An Edge-Native Federated Learning Approach

Internet of Medical Things (IoMT) devices operate under strict resource constraints while handling highly sensitive health data, making security and privacy critical concerns. Federated learning (FL) further complicates this landscape, as model updates exchanged during training may unintentionally expose private medical information. Emerging quantum computing capabilities threaten the long-term viability of conventional lightweight cryptographic mechanisms, motivating the integration of Post-Quantum Cryptography (PQC) into IoMT systems. This article discusses key enabling technologies for quantum-resilient IoMT, including post-quantum key establishment, lightweight encryption, and edge-native orchestration. We propose a scalable Kubernetes-based framework that integrates PQC into FL-enabled IoMT environments and validate it on a Raspberry Pi testbed. Results demonstrate that distributed cryptographic processing significantly reduces latency compared to sequential designs while maintaining feasible resource overhead. The primary contribution of this work lies in the design and validation of a secure orchestration and communication framework for FL-enabled IoMT systems. We conclude by outlining future directions toward energy-aware architectures, intelligent security optimization, and resilient next-generation Intelligent Internet of Medical Things (IIoMT) ecosystems.

Post-Quantum Secure Federated DeFi for Inclusive Banking

Recent advances in error-corrected qubits have accelerated the timeline for practical quantum computing. It poses a threat to cryptographic primitives used to secure financial systems, government infrastructure, communication networks, and DeFi (Decentralized Finance) ecosystems. This paper introduces a post-quantum secure federated DeFi framework that enables inter-bank collaboration to improve the inclusivity of individuals underserved by local lenders due to limited financial histories. Multiple banks contribute encrypted information batches to a virtual server, where lattice-based Fully Homomorphic Encryption (FHE) enables end-to-end homomorphic computation. The server fuses local data-driven probabilistic assessments, expert beliefs, and verifiable evidence generated by the NASA-IBM Prithvi Geospatial Foundation Model (GFM), in encrypted format. Decentralized technologies are employed to ensure tamper-proof evidence and auditable accountability for all encrypted data exchanges between institutions and the server. The framework is tested on agricultural lending decisions for rural borrowers in Virginia.