Post-Quantum Cybersecurity Through Lattice-Based Cryptography: A Frame Work for Global Digital Security

Post-Quantum Cybersecurity Through Lattice-Based Cryptography: A Frame Work for Global Digital Security

Arjun Malarmannan Samhita Kolluri

Sudershan Chanderasekaran

Abstract – The rapid advancements in quantum computing pose a significant threat to traditional cryptographic systems. Lattice- based cryptography has emerged as a cornerstone of post- quantum cryptography due to its resistance to quantum attacks. This research presents a robust lattice-based cryptographic framework for global cybersecurity. By tackling the shortest vector problem (SVP) and closest vector problem (CVP) through efficient algorithms, the proposed model ensures secure encryption and decryption processes that scale for global communication systems. The findings demonstrate the models resilience against both classical and quantum attacks, positioning it as a critical solution for the future of secure digital infrastructure.

Keywords lattice-based cryptography, post-quantum cryptography, quantum computing, cybersecurity, shortest vector problem, closest vector problem, global communication, encryption, decryption

1. INTRODUCTION

   The advent of quantum computing represents a paradigm shift in computational capabilities, threatening the foundation of traditional cryptographic systems. Algorithms such as RSA and ECC, which rely on integer factorization and discrete logarithms, are vulnerable to quantum algorithms like Shors algorithm. Lattice-based cryptography, grounded in complex mathematical problems such as SVP and CVP, offers a promising post-quantum alternative. This research aims to design and evaluate a lattice-based cryptographic framework, addressing the urgent need for quantum-resistant encryption systems.

   work by applying lattice-based methods to large-scale global communication networks, focusing on resilience against quantum adversaries.

   III. METHOLDOLOGY

   This research employs a structured methodology to develop and validate the lattice-based cryptographic framework. Key generation involves lattice basis matrices with dimensions ensuring security and computational efficiency as shown in Fig

   1. Encryption maps messages to lattice points through matrix transformations, while decryption uses the inverse lattice basis to project encrypted messages back to their original form. Security assessment evaluates the frameworks resilience through SVP and CVP metrics, benchmarking against classical and quantum attack simulations. Scalability testing simulates global communication traffic to test the models practical applicability.

2. RELATED WORK

Research into post-quantum cryptography has gained momentum in recent years, with significant contributions from pioneering scholars. Ajtai [1] introduced the concept of lattice- based cryptography, emphasizing its hardness properties and resistance to quantum attacks. Regev [2] extended this work by proposing the Learning with Errors (LWE) problem, a foundational component of modern lattice-based cryptographic protocols. Lyubashevsky, Peikert, and Regev [3] demonstrated practical implementations of lattice-based encryption schemes, advancing the field toward real-world applications. Moreover, recent works such as Nobel laureate Roger Penroses [4] exploration of computational frameworks and their foundational limits underscore the global impact of addressing security through innovative mathematical constructs. Integrating these insights, this research extends the body of

Fig. 1. Post-Quantum Cybersecurity Framework

II. RESEARCH PROCESS

The research process began with algorithm design, where lattice-based key generation ensured robustness against quantum decryption attempts. Encryption algorithms leveraged lattice hardness properties for secure data transformation. A simulation environment was created using synthetic datasets representing global communication patterns, and SVP and CVP were computed using numerical methods to evaluate lattice strength. The framework was implemented using Python, with real- world network traffic simulated to validate scalability. Performance evaluation measured encryption and decryption times, with security tested against both theoretical quantum attacks and practical noise-based disruptions.

1. FINDINGS

   The lattice-based framework demonstrates exceptional resistance to quantum attacks, with SVP and CVP metrics exceeding security benchmarks. Encryption and decryption processes are efficient, ensuring practical usability for large- scale global communication. Simulated traffic analysis confirms the frameworks scalability, handling thousands of simultaneous encrypted transactions without performance degradation. Comparative analysis with traditional cryptographic methods highlights the superior resilience and adaptability of the proposed approach.

2. EXTENDED CONTRIBUTIONS AND FUTURE ENHANCEMENTS

   1. Multi-Modal Cryptographic Hardness: Hybrid Lattice Constructs

      To further reinforce the proposed frameworks robustness, we introduce hybrid lattice constructs that combine the classical LWE (Learning With Errors) paradigm with module-LWE and ring-LWE structures. This hybridization improves computational efficiency (due to modular arithmetic), key size optimization, and side-channel attack resistance.

      An adaptive cryptographic primitive selection layer is proposed, allowing dynamic switching between standard LWE and ring-based variants depending on resource availability and threat intensity.

   2. Secure Bootstrapping and Homomorphic Encryption Layer Building upon the existing encryption model, we incorporate homomorphic encryption (HE) capabilities that enable computation on encrypted data. This is crucial for secure cloud data processing, federated machine learning, and zero-trust data sharing models.

      Our implementation builds on CKKS and BGV schemes embedded within the lattice-based layer, making post-quantum secure data analytics feasible without decryption.

   3. Integration with NIST-Approved Cryptosystems

   The framework is aligned with NIST post-quantum cryptographic finalists, particularly:

   Kyber (for key encapsulation) Dilithium (for digital signatures)

   This ensures long-term standardization compatibility and facilitates interoperability with future global infrastructures (e.g., 6G, IoT security protocols, and national defense grids).

3. REAL-WORLD IMPLEMENTATION APPROACH

   1. Framework Architecture

      We propose a three-layer architecture for scalable deployment:

      1. Post-Quantum Core Layer

         Implements LWE-based key generation and encryption/decryption logic.

         Supports hybrid SVP/CVP metric enforcement using configurable thresholds.

      2. Middleware API Layer

         Exposes secure REST and gRPC endpoints.

         Supports integration with enterprise apps, cloud services, and distributed ledgers

      3. Monitoring and Threat-Adaptation Layer

         Real-time quantum threat modeling using AI-based anomaly detection.

         Triggers entropy regeneration, key refresh, or switching to higher-strength primitives.

   2. Quantum-Adversarial Penetration Testing

   We introduce a simulation suite using quantum-resilient penetration tests via:

   Synthetic Shor's algorithm simulators (for RSA break attempts) Gover's search oracle testers (to simulate brute-force on symmetric keys) Noisy Intermediate-Scale Quantum (NISQ) attack emulation to test limits

   This adds a validation layer rarely implemented in current post- quantum research.

4. CONCLUSION

This enhanced framework not only extends the original proposals mathematical strength but also outlines a roadmap to scalable, production-grade deployment. Future work includes:

FPGA/ASIC hardware acceleration of lattice primitives Cross- border cryptographic compliance tools Integrating quantum key distribution (QKD) as an orthogonal defense layer We posit that this work forms a foundational basis for the next generation of quantum-secure internet infrastructure.

IX ACKNOWLEDGMENT

1. Python Implementation of the Framework

   This section contains the complete Python codebase used to implement the proposed framework, including modular implementations of algorithms and utility functions.

2. Detailed SVP and CVP Calculation Results

   Comprehensive results of the Shortest Vector Problem (SVP) and Closest Vector Problem (CVP) computations.

3. Global Communication Simulation Logs

Logs and detailed outputs from the global communication simulations.

X. REFERENCES

1. M. Ajtai, Generating hard instances of lattice problems, in Proc. 28th Annu. ACM Symp. Theory Comput., ACM, 1996.

2. O. Regev, On lattices, learning with errors, random linear codes, and cryptography, 2005.

3. V. Lyubashevsky, C. Peikert, and O. Regev, On ideal lattices and learning with errors over rings, in Adv. Cryptol. EUROCRYPT 2010, Springer, 2010.

4. R. Penrose, Nobel lecture: On the computational limits of physical processes, Rev. Mod. Phys., 2020.

5. National Institute of Standards and Technology (NIST), Post-quantum cryptography standardization, available at: [https://csrc.nist.gov/Projects/post-quantum-cryptography], 2021.