Optimizing Post-Quantum LWE Encryption for Large Image Data: An Integrated Compression and Algorithmic Acceleration Framework

Authors: MD. Mehedi Hasan, Md. Nasir Uddin
Supervisor: A. K. M. Fakhrul Hossain, Lecturer, Department of CSE
Institution: Shahjalal University of Science and Technology, Sylhet, Bangladesh

Abstract

Post-quantum cryptography (PQC) has a significant computational overhead because lattice-based methods, particularly Learning With Errors (LWE), require large matrix operations and the manipulation of high-dimensional data. This computational burden is further intensified when cryptographic systems operate on large-scale image data.

We present a comprehensive hybrid cryptographic preprocessing and acceleration framework that integrates:

• Image compression techniques: Run-Length Encoding (RLE), Huffman coding, YCbCr color space transformations with chroma subsampling
• Algorithmic acceleration: Strassen's matrix multiplication algorithm

Key Results

Metric	Achievement
Data Volume Reduction	41.19% average
Compression Type	Lossless (PSNR = ∞)
Security	Full post-quantum guarantees

Background

Learning With Errors (LWE)

The LWE problem forms the foundation of our encryption scheme. Given a secret vector $\mathbf{s} \in \mathbb{Z}_q^n$, the LWE distribution produces samples:

$$(\mathbf{a}, b = \langle \mathbf{a}, \mathbf{s} \rangle + e) \in \mathbb{Z}_q^n \times \mathbb{Z}_q$$

where $\mathbf{a}$ is uniformly random and $e$ is a small error term.

Color Space Conversion (YCbCr)

Standard digital conversion from RGB to YCbCr:

$$\begin{bmatrix} Y \\ Cb \\ Cr \end{bmatrix} = \begin{bmatrix} 0.299 & 0.587 & 0.114 \\ -0.169 & -0.331 & 0.500 \\ 0.500 & -0.419 & -0.081 \end{bmatrix} \begin{bmatrix} R \\ G \\ B \end{bmatrix} + \begin{bmatrix} 0 \\ 128 \\ 128 \end{bmatrix}$$

Strassen Matrix Multiplication

Strassen's algorithm reduces matrix multiplication complexity from $O(n^3)$ to $O(n^{2.807})$:

$$C = A \times B$$

Using 7 multiplications instead of 8 for $2 \times 2$ submatrices.

Proposed Architecture

Pipeline Overview

1. RGB to YCbCr Conversion - Color space transformation
2. Chroma Subsampling - 4:2:0 subsampling for Cb/Cr channels
3. Three-Stage Lossless Encoding:
   • Differential Pulse Code Modulation (DPCM)
   • Run-Length Encoding (RLE)
   • Huffman Coding
4. LWE Encryption Core - With plaintext batching
5. Strassen Matrix Multiplication - Accelerated encryption

Compression Pipeline Results

Stage	Size Reduction
YCbCr + Subsampling	~50%
DPCM	Variable
RLE	Pattern-dependent
Huffman	Entropy-optimal
Total	41.19% average

Experimental Results

Compression Ratios

Tested across multiple image datasets with varying complexity:

• High-frequency images: 30-35% reduction
• Natural images: 40-45% reduction
• Synthetic/uniform images: 50%+ reduction

Image Quality Verification

All reconstructed images achieved:

• PSNR = ∞ (perfect reconstruction)
• SSIM = 1.0 (structural similarity)
• MSE = 0 (zero error)

Conclusion

This framework establishes a practical and scalable paradigm for deploying quantum-resistant encryption on resource-constrained platforms. The successful unification of compression and cryptographic acceleration provides a powerful template for future PQC implementations.

Future Work

• Extension to Ring-LWE and Module-LWE schemes
• Hardware acceleration via FPGAs or GPUs
• Real-time throughput optimization for high-volume data streams

Keywords

LWE, Post-quantum cryptography, Run-length encoding, Huffman coding, Strassen algorithm, Color space transformation, Chroma subsampling, Image Compression, Lattice cryptography, DPCM, Cryptographic acceleration.