Optimizing Post-Quantum Cryptography for IoT: A Lazy Reduction and Residue Number System Approach

Md Sazzad Hossain

doi:10.36948/ijfmr.2024.v06i05.78519

Optimizing Post-Quantum Cryptography for IoT: A Lazy Reduction and Residue Number System Approach

Author(s)	Mr. Md Sazzad Hossain
Country	United States
Abstract	We propose a new optimization framework for post-quantum cryptography (PQC) in IoT devices, which tackles the computational inefficiency of lattice-based cryptographic operations by employing advanced number-theoretic techniques. The proposed method merges lazy reduction and residue number systems (RNS) to reduce modular arithmetic overhead without compromising quantum resistance, which is essential for resource-limited IoT settings. Lazy reduction postpones modular operations in polynomial multiplication and number-theoretic transforms (NTT), thereby decreasing the computational depth substantially while preserving the original algebraic structure. Moreover, RNS breaks down large-integer arithmetic into parallel operations at the residue level, which removes carry propagation and supports effective execution on low-power microcontrollers. The system upholds alignment with NIST PQC standards, including CRYSTALS-Kyber, by preserving initial security parameters and hardness assumptions. Empirical assessments conducted on ARM Cortex-M4 systems show a 30% decrease in NTT computational overhead and a 22% gain in energy performance relative to standard implementations. The hardware-software co-design features ASIC-optimized NTT cores and parallel RNS arithmetic units, synthesized for 40nm CMOS technology to balance performance and power consumption. This work stands out by distinctly merging lazy reduction and RNS in lattice-based PQC, thereby delivering a practical approach to safeguard IoT ecosystems from quantum threats. The modular architecture guarantees smooth compatibility with current IoT cryptographic systems, which positions it as a suitable option for broad implementation in IoT solutions designed for long-term viability.
Keywords	Post-Quantum Cryptography (PQC), Internet of Things (IoT), Lattice-Based Cryptography, Lazy Reduction, Residue Number System (RNS), Number-Theoretic Transform (NTT), CRYSTALS-Kyber, NIST PQC Standards, Modular Arithmetic Optimization, ARM Cortex-M4, ASIC Optimization, Hardware-Software Co-Design, Quantum-Resistant Cryptography, Low-Power Cryptographic Systems, Parallel Arithmetic Processing, Energy-Efficient Computing, CMOS Cryptographic Architecture, Resource-Constrained Devices, Secure IoT Systems, Polynomial Multiplication Optimization
Field	Computer > Network / Security
Published In	Volume 6, Issue 5, September-October 2024
Published On	2024-10-05
DOI	https://doi.org/10.36948/ijfmr.2024.v06i05.78519

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Optimizing Post-Quantum Cryptography for IoT: A Lazy Reduction and Residue Number System Approach

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