Published Research
Advances in Decision Sciences · DOI: 10.47654/v30y2026i3p184-214
Abstract
This paper addresses a core decision problem in healthcare data governance: how should 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 LFSR-based encryption system.
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 cipher.
This expands the key space from 2ⁿ−1 to 3ⁿ−1 states
while maintaining O(N log N) computational complexity.
Evaluated on kidney ultrasound, brain MRI, and multiple sclerosis MRI across 10–15 images per modality. Encrypted images exhibit near-uniform histograms and near-zero pixel correlations (≤ 0.022), with correct-key decryption recovering SSIM of 0.9903–1.0000.
Authors
Trapti Sharma · Ayush Ranjan · Harvinder Singh · Rajit Nair
VIT Bhopal University, India
Hasan Alkahtani · Sami Morsi · Ahmed A.F. Osman · Theyazn H.H. Aldhyani
King Faisal University, Saudi Arabia
Key Results
Interactive Demo
Watch the GF(3) ternary LFSR shift and generate a pseudo-random keystream. Each cell holds a value in {0, 1, 2} — the three ternary states.
State registers shown in trit form (0, 1, 2) · Feedback polynomial: x⁸ + x⁶ + x⁴ + x² + 1 over GF(3)
Original Contributions
A formally grounded, evidence-based framework mapping LFSR configuration variables (n, P) to security-versus-cost trade-offs across three healthcare deployment tiers. Minimax-regret analysis provides robust guidance under attacker capability uncertainty. Directly applicable to HIPAA/GDPR compliance.
The first deployment of ternary logic (GF(3)) within an LFSR-based cipher specifically for medical image protection. Expands key space from 2ⁿ−1 to 3ⁿ−1 states while maintaining low computational overhead — making it deployable on embedded IoT medical devices.
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. The low computational overhead of the ternary LFSR cipher makes the framework practically deployable on embedded and IoT-based 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 choices directly impact regulatory compliance, patient privacy, and operational efficiency.
How to Cite