A New Approach for Image SecurityEnhancement Using Ternary Logic LinearFeedback Shift Register for CryptographicApplications

Abstract

Purpose: This paper addresses a core decision problem in healthcare data governance: how should healthcare decision-makers optimally select encryption parameters under resource and threat-model constraints? To answer this, a formal multi-criteria decision framework is developed and instantiated through a novel ternary linear feedback shift register (LFSR)-based encryption system, providing clinicians and security engineers with principled, quantitative parameter-selection guidance for lightweight image-encryption deployment on resource-constrained medical devices.

Design/Methodology/Approach: The proposed method extends traditional binary LFSRs to the ternary domain GF(3), operating over three logic states {0, 1, 2}, to generate pseudo-random keystreams that drive a pixel-permutation cypher. The system was evaluated on 10–15 images per modality across three clinically distinct modalities: kidney ultrasound, brain MRI, and multiple sclerosis (MS) MRI; reported metrics correspond to the image whose scores were closest to the modality average, ensuring representative rather than cherry-picked results. Evaluation used standard security metrics including NPCR, UACI, information entropy, MSE, PSNR, SSIM, and pixel-correlation coefficients.

Findings: The model achieves a Number of Pixels Change Rate (NPCR) of 98.04% and entropy of 6.80 bits for kidney ultrasound images and a Unified Average Changing
Intensity (UACI) of 27.96% for brain MRI images. Encrypted images exhibit nearuniform histograms and near-zero pixel correlation coefficients (≤ 0.022), confirming strong randomness. Correct-key decryption recovers the original image with SSIM values of 0.9903–1.0000 and PSNR values of 44.52–52.21 dB. Incorrect-key decryption produces entirely unintelligible output, validating key sensitivity. The entropy gap below the 8-bit theoretical maximum is attributed to the permutation-only design, which preserves pixel intensity values; this limitation and the path towards a diffusion layer are discussed.

Originality/Value: This work makes two original contributions. The primary contribution is a formally grounded, evidence-based decision framework that maps LFSR
configuration variables (n, P) to measurable security-versus-cost trade-offs across three healthcare deployment tiers, enabling risk-based governance of medical image encryption. The secondary contribution is the ternary LFSR cipher itself — the first deployment of GF(3) logic within an LFSR-based cypher for medical image protection — which serves as the concrete case study instantiating the decision framework, expanding the key space from 2n − 1 to 3n − 1 states while maintaining O(N logN) computational complexity.

Implications: The decision framework gives healthcare administrators and security engineers a structured, evidence-based basis for encryption parameter selection, directly supporting risk-based governance and regulatory compliance (e.g., HIPAA, GDPR). The minimax-regret analysis provides robust configuration guidance even under uncertainty about attacker capability and device heterogeneity. The low computational overhead of the ternary LFSR cipher makes the framework practically deployable on embedded and IoTbased medical devices. This work advances decision science methodology by formalizing parameter-selection under resource constraints and threat-model uncertainty—a canonical multi-criteria decision problem—and demonstrating its application to healthcare data
governance, where encryption configuration choices directly impact regulatory compliance, patient privacy protection, and operational efficiency under bounded computational budgets.