Securing AI in a Post-Quantum World

Author: Denis Avetisyan

A new framework leverages the principles of Zero Trust and category theory to protect artificial intelligence models against emerging quantum threats, even on limited-resource devices.

The system employs a Zero Trust Architecture-secured with quantum-resistant SSL encryption and time-stamped requests-that isolates privileged resources within an authenticated Local Area Network zone, ensuring access is strictly limited to pre-approved entities.

This paper details a categorical framework integrating post-quantum cryptography and Zero Trust architecture for secure and efficient AI model protection, with a focus on edge computing applications like the ESP32.

The increasing prevalence of AI models, coupled with the looming threat of quantum computing, creates a critical need for robust and future-proof security paradigms. Addressing this challenge, our work, ‘Categorical Framework for Quantum-Resistant Zero-Trust AI Security’, introduces a novel integration of post-quantum cryptography and zero trust architecture, uniquely formalized using category theory to model cryptographic workflows and trust policies. This approach enables fine-grained, adaptive security for AI models, particularly on resource-constrained edge devices like the ESP32, demonstrably achieving high performance and rejecting all unauthorized access attempts. Will this categorical approach unlock new levels of formal verification and trust in increasingly complex AI systems?

Beyond Classical Cryptography: A Necessary Evolution

The foundations of modern digital security, reliant on algorithms like RSA and ECC, face an existential threat from the rapidly developing field of quantum computing. These algorithms, while currently secure, depend on the computational difficulty of certain mathematical problems – problems that Shor’s algorithm, executed on a sufficiently powerful quantum computer, can solve efficiently. This breakthrough renders commonly used encryption methods vulnerable to decryption and forgery, potentially exposing sensitive data – from financial transactions to national security information. Consequently, a proactive transition to post-quantum cryptography (PQC) is crucial. PQC focuses on developing cryptographic systems that are resistant to attacks from both classical and quantum computers, utilizing mathematical problems believed to be intractable even for quantum algorithms. This shift isn’t simply an upgrade; it’s a fundamental reimagining of digital security protocols, demanding rigorous testing and standardization to ensure future resilience in a world increasingly shaped by quantum capabilities.

Conventional security systems, often reliant on algorithms like RSA and ECC, are increasingly challenged by a rapidly shifting threat landscape. These established methods frequently lack the agility to respond effectively to newly discovered vulnerabilities or sophisticated attack vectors. Furthermore, providing provable guarantees of long-term security proves difficult, as reliance on computational hardness-the assumption that breaking an algorithm requires impractical amounts of computing power-is constantly undermined by advances in computing technology. The static nature of many current systems necessitates costly and disruptive overhauls when vulnerabilities are discovered, and often, the security offered is based on heuristics rather than rigorous mathematical proof, creating a precarious situation as adversaries develop more powerful tools and techniques.

The future of digital security hinges on a fundamental shift in cryptographic design, moving beyond systems built on mathematical problems easily solved by future quantum computers. Current approaches often prioritize static security – a fixed defense against known threats – but a truly robust system must embrace dynamic security. This necessitates a paradigm that prioritizes both resilience – the ability to withstand attacks even when compromised – and adaptability, allowing the system to evolve its defenses in response to newly discovered vulnerabilities or emerging threats. Such a system wouldn’t rely on the secrecy of algorithms, but on the continuous and automated updating of cryptographic primitives, effectively raising the bar for attackers and ensuring long-term confidentiality and integrity of data even in a post-quantum world. This proactive approach represents a move from simply defending against attacks to actively anticipating and neutralizing them, guaranteeing a more secure digital future.

Statistical divergence heatmaps reveal that replacing Gaussian noise with deterministic noise generated via Engel expansions significantly alters ciphertext distributions in an LWE cryptosystem, as measured by Wasserstein distance and Kullback-Leibler divergence across varying parameters like noise standard deviation, modulus, and dimension.

Category Theory: A Foundation for Cryptographic Rigor

Category theory offers a formalized system for representing cryptographic primitives – such as encryption, decryption, hashing, and digital signatures – as mathematical objects and their relationships as morphisms. This allows for the analysis of cryptographic systems at a high level of abstraction, independent of specific implementations. Crucially, the compositional nature of category theory facilitates the rigorous verification of how these primitives interact within larger protocols; by establishing that a system is built from correctly composed categories, assurances about its overall security can be derived. This approach moves beyond ad-hoc security arguments to a formal, mathematical basis for evaluating and constructing secure cryptographic systems, enabling proofs of correctness and identifying potential vulnerabilities arising from compositional errors.

Category theory facilitates crypto-agility by representing cryptographic algorithms as morphisms within abstract categories, focusing on relationships rather than specific implementations. This abstraction allows for the substitution of one algorithm for another – such as transitioning from RSA to elliptic-curve cryptography – provided the new algorithm satisfies the same categorical properties and interface. Because the system is designed around these abstract interfaces, changes to underlying algorithms do not require modifications to the overall system architecture, reducing the costs and risks associated with cryptographic updates and enabling a more flexible and future-proof security infrastructure.

The application of `Category_Theory_Primitives` facilitates formal verification of security protocols by enabling the representation of cryptographic components as abstract morphisms and their compositions as higher-order operations. This approach allows for rigorous mathematical proof of security properties, such as confidentiality and integrity, independent of specific implementations. Recent implementations utilizing these primitives have demonstrated a significant improvement in computational efficiency; specifically, key operations that previously exhibited $O(n^2)$ complexity have been reduced to $O(n)$ complexity, representing a substantial performance gain for large datasets and resource-constrained environments.

Simulations of an LWE cryptosystem modeled as a wiretap channel reveal that maintaining secure communication requires a noise advantage that increases with eavesdropper signal-to-noise ratio (SNR), and demonstrate achievable secure rates across varying SNR regimes and noise advantages, ultimately quantifying the system's robustness compared to classical secure communication. — Simulations of an LWE cryptosystem modeled as a wiretap channel reveal that maintaining secure communication requires a noise advantage that increases with eavesdropper signal-to-noise ratio (SNR), and demonstrate achievable secure rates across varying SNR regimes and noise advantages, ultimately quantifying the system’s robustness compared to classical secure communication.

ZT-AI: A Quantum-Resistant System in Practice

The $ZT\_AI\_System$ utilizes a Zero Trust Architecture, establishing secure communication through Lattice-based Learning With Errors ($LWE$) encryption. Performance metrics indicate an average encryption time of 10.97 milliseconds and a decryption time of 2.89 milliseconds. This approach to cryptography relies on the presumed hardness of solving certain problems in lattice structures, offering a potential defense against attacks from quantum computers. The system’s implementation of $LWE$ focuses on minimizing computational overhead while maintaining a high level of security for data in transit and at rest.

The $ZT\_AI\_System$ is designed for deployment on the $ESP32\_Platform$, a microcontroller commonly used in embedded systems due to its low cost and integrated features. This implementation demonstrates the system’s viability in resource-constrained environments, achieving a peak power consumption of 479mW during operation. This power profile allows for battery-powered or energy-harvesting applications, expanding the potential deployment scenarios for a quantum-resistant security solution beyond traditional server infrastructure. The selection of the $ESP32\_Platform$ validates the system’s optimization for low-power, embedded device integration without compromising its core cryptographic functionality.

Engel Expansion is a security technique implemented within the $ZT\_AI\_System$ to mitigate lattice reduction attacks, a primary threat to Lattice-based cryptography. This technique introduces a controlled expansion of the lattice, increasing the computational complexity required for successful attacks without significantly impacting performance. Benchmarks demonstrate that Engel Expansion allows the system to sustain 91.86% of free RAM during operational processes, indicating efficient memory management alongside enhanced security. The technique effectively raises the barrier against cryptanalysis by increasing the difficulty of finding short vectors within the lattice, thereby strengthening the overall cryptographic defenses of the $ZT\_AI\_System$.

Latency distributions for LWE parameter sets reveal a trade-off between security level and performance, with lower security settings dominated by AI inference and higher security settings increasingly burdened by cryptographic overhead, though optimized parameters can achieve a more balanced profile.

Formal Verification and Security Guarantees: Beyond Mere Testing

The integrity of the ZT_AI_System hinges on a rigorous process of formal verification, a technique deeply rooted in the abstract mathematical framework of category theory. This isn’t simply testing; it’s a provable demonstration of the system’s correctness and security. By modeling the system’s components and their interactions as mathematical objects – specifically, ‘morphisms’ and ‘categories’ – researchers can mathematically prove that the system will behave as intended under all possible conditions. This approach transcends traditional software validation, which relies on testing a finite number of scenarios, and instead offers a definitive guarantee against vulnerabilities and unexpected behavior. The application of category theory allows for compositional reasoning – verifying individual components and then confidently assembling them into a secure whole – ultimately establishing a foundation of trust in the ZT_AI_System’s operations and resilience against malicious attacks.

The ZT_AI System incorporates a proactive defense against $Lattice\_Reduction\_Attacks$, a significant threat to cryptographic systems. This is achieved through the strategic application of $Engel\_Expansion$, a mathematical technique that effectively increases the dimensionality of the lattice space. By expanding the lattice, the system dramatically raises the computational complexity required for an attacker to successfully reconstruct the secret key. This method doesn’t simply increase the difficulty; it fundamentally alters the attack surface, forcing adversaries to confront an exponentially larger search space. Consequently, even with substantial computational resources, the feasibility of a lattice reduction attack is severely diminished, providing a robust layer of security for the ZT_AI System’s sensitive data and operations.

The system’s security architecture rests upon the foundations of Information-Theoretic Security, moving beyond computational complexity to achieve provable guarantees of confidentiality. Leveraging the Wiretap Channel Model – a concept originally developed for communication theory – the system effectively creates a scenario where an eavesdropper receives no information about the transmitted data, even with unlimited computational power. This is accomplished through a carefully engineered separation of signal and noise, ensuring that any attempt at unauthorized access yields only random data. Rigorous testing demonstrates a 100% rejection rate of all simulated access attempts, consistently achieved with sub-millisecond latency, establishing a robust defense against evolving cyber threats and providing a uniquely secure environment for sensitive data processing.

Analysis of error and rejection rates under varying noise levels and system parameters (lattice dimension, modulus size, and base noise) demonstrates that the categorical error rate increases with adversarial noise while the traditional error rate remains negligible, suggesting the system effectively rejects most insecure transmissions.

Beyond Resilience: Towards Adaptable and Trustworthy Systems

The principles of functional programming, deeply rooted in the abstract mathematics of category theory, offer a powerful pathway towards building inherently more secure and manageable systems. By emphasizing immutability and pure functions – those without side effects – functional approaches drastically reduce the complexity often associated with software vulnerabilities. This paradigm encourages the decomposition of problems into smaller, independent modules, each easily testable and verifiable. The resulting code is not only more modular but also less prone to errors arising from shared state or unexpected interactions. Furthermore, the mathematical foundations of functional programming allow for formal verification – proving the correctness of code with rigorous certainty – offering a level of assurance difficult to achieve with traditional imperative programming styles. This inherent structure simplifies auditing and enhances trustworthiness, especially critical in security-sensitive applications where even minor flaws can have significant consequences.

The core tenets of Zero Trust AI – continuous verification, least privilege access, and the assumption of compromise – are proving broadly applicable beyond artificial intelligence systems. These principles are increasingly vital for securing a diverse range of critical infrastructure, including energy grids, financial networks, and healthcare systems. By shifting from perimeter-based security to a model that validates every user, device, and transaction, organizations can significantly reduce the attack surface and limit the blast radius of potential breaches. This proactive approach, initially developed to address the unique vulnerabilities of AI, offers a pathway towards building more resilient and adaptable security architectures capable of withstanding increasingly sophisticated cyber threats, and fostering a future where trust is earned, not assumed.

The longevity of digital security hinges on proactive advancements in both formal verification and post-quantum cryptography. Current encryption methods are increasingly vulnerable to anticipated quantum computing capabilities, necessitating a shift towards algorithms resistant to these emerging threats. Recent investigations have focused on optimizing key sampling processes within these new cryptographic frameworks, achieving a substantial improvement from a linear time complexity of O(n) to a constant time complexity of O(1). This optimization, facilitated by novel approaches to formal verification, drastically reduces computational overhead and enhances the scalability of secure systems. Consequently, continued research in these areas isn’t simply about fortifying existing defenses, but about establishing a foundation for trustworthy and adaptable digital infrastructure capable of withstanding future challenges and ensuring ongoing data integrity.

The presented framework prioritizes a reduction of complexity in securing AI models at the edge. It achieves this through the rigorous application of category theory, formalizing both Post-Quantum Cryptography and Zero Trust principles. This mirrors Donald Davies’ assertion that “Simplicity is the ultimate sophistication.” The framework doesn’t aim for impenetrable complexity, but rather a distilled, verifiable security structure, particularly suited for resource-constrained devices like the ESP32. The emphasis on formal verification, inherent in the categorical approach, embodies a commitment to eliminating unnecessary layers – a pursuit of clarity as compassion for cognition, ensuring robust security without prohibitive overhead.

What Remains?

The presented framework, while achieving a degree of formal rigor, merely addresses the symptom of insecurity, not its root. Category theory, employed here as a tool for structuring complexity, reveals the inescapable truth: any formal system, however elegant, is only as secure as its foundational assumptions. The reliance on lattice-based cryptography, while currently resistant to known quantum attacks, is not a perpetual shield. Future algorithmic advancements, or even entirely new computational paradigms, may invalidate these protections.

The practical limitation-resource constraint-is not a technical hurdle to be overcome with optimization, but a fundamental reality. Security, ultimately, demands resources. The pursuit of “lightweight” cryptography is a constant negotiation between acceptable risk and achievable efficiency. This work, therefore, serves primarily as a demonstration of possible security, not its guarantee.

Future research should not focus on extending this framework, but questioning its necessity. The truly secure system is the one that does not exist, or the one that renders itself irrelevant through simplicity. The problem isn’t building better walls, but eliminating the need for them.

Original article: https://arxiv.org/pdf/2511.21768.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/