MedPQC: Hybrid Post-Quantum Key Encapsulation with Lorenz Chaotic Diffusion for Authenticated Medical Image Encryption

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Authors and Affiliation

• Muhammad Khubaib Ahmad
  • Email: khubaib.ahmad@inference-lab.org | muhammadkhubaibahmad854@gmail.com
  • Affiliation: INFERENCE Lab
• Muzammil Shadab
  • Email: muzammil.shadab@inference-lab.org
  • Affiliation: INFERENCE Lab

Repository: https://github.com/Inference-LAB/medPQC

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Abstract and Overview

Modern Picture Archiving and Communication Systems (PACS) and cloud-native Telemedicine infrastructures transport high-resolution patient radiological scans across public network perimeters. Classical public-key schemes (RSA, standard Diffie-Hellman, ECDH) remain acutely vulnerable to quantum polynomial-time Shor factorization and retroactive Harvest Now, Decrypt Later (HNDL) state adversary collection.

MedPQC provides an authenticated, post-quantum resilient, and cryptographically sound framework engineered explicitly for radiological datasets. It marries:

1. Hybrid Key Exchange: Dual-defense encapsulation combining classical Elliptic Curve Diffie-Hellman over NIST P-256 with Ring Learning With Errors / Module-Lattice-Based Key Encapsulation (ML-KEM / NIST FIPS 203), combined using an HKDF-SHA3-512 key derivation function.
2. JIT-Accelerated Continuous Chaotic Engine: Fourth-order Runge-Kutta (RK4) integration of the three-dimensional Lorenz dynamical system ($\sigma=10, \rho=28, \beta=8/3$, positive Lyapunov exponent $\lambda_1 = +0.9066$), compiled to native machine code via Numba JIT.
3. Cryptographic Entropy Sponge: SHA3-based continuous distillation guaranteeing high statistical entropy and passing all 15 NIST SP 800-22 randomness tests.
4. Bijective Permutation & Non-Linear Diffusion: Chaotic Fisher-Yates coordinate permutation followed by a 3-round Cipher Block Chaining (CBC)-like bitplane diffusion layer that completely destroys adjacent horizontal, vertical, and diagonal pixel correlations.
5. Double-Layer Authenticated Encryption (AEAD): AES-256-GCM combined with an outer HMAC-SHA3-256 digest operating under a strict verify-then-decrypt paradigm to defeat Chosen-Ciphertext Attacks (IND-CCA2).
6. Lossless Clinical Preservation: Exact preservation of 8-bit and native 16-bit medical data (uint8, int16, uint16, Hounsfield Units) with zero numerical degradation ($\text{MSE} = 0.000000$).

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Architecture Specification

+--------------------------------------------------------------------------------------------------+
|                                    MedPQC SYSTEM ARCHITECTURE                                    |
+--------------------------------------------------------------------------------------------------+
|                                                                                                  |
|   1. HYBRID KEY AGREEMENT LAYER                                                                  |
|   +--------------------------+   +-------------------------------+                              |
|   |   Classical NIST P-256   |   | Post-Quantum ML-KEM / RLWE    |                              |
|   |         ECDH             |   |        (NIST FIPS 203)        |                              |
|   +------------+-------------+   +---------------+---------------+                              |
|                |                                 |                                               |
|                +----------------+----------------+                                               |
|                                 |                                                                |
|                                 v                                                                |
|                    [ HKDF-SHA3-512 Combiner ]                                                    |
|                                 |                                                                |
|                                 +------------------------------+                                 |
|                                 |                              |                                 |
|                                 v                              v                                 |
|                     K_enc, K_mac (64 bytes)        Chaos Initial Seed S_chaos                    |
|                                 |                              |                                 |
|   2. CHAOTIC CORE               |                              v                                 |
|                                 |                  [ Lorenz RK4 Integrator ]                     |
|                                 |                  (Numba JIT: fastmath=True)                    |
|                                 |                              |                                 |
|                                 |                              v                                 |
|                                 |                  [ NIST SP 800-22 Sponge ]                     |
|                                 |                              |                                 |
|                                 |                 +------------+------------+                    |
|                                 |                 |                         |                    |
|   3. PIXEL SCRAMBLING           |                 v                         v                    |
|      & DIFFUSION                |       Fisher-Yates Permutation   3-Round CBC-XOR Diffusion     |
|                                 |                 |                         |                    |
|                                 |                 +------------+------------+                    |
|                                 |                              |                                 |
|                                 |                              v                                 |
|                                 |                   Permuted & Diffused Array                    |
|                                 |                              |                                 |
|   4. AUTHENTICATED WRAPPER      v                              v                                 |
|                         [ AES-256-GCM ] <----------------------+                                 |
|                                 |                                                                |
|                                 v                                                                |
|                        [ HMAC-SHA3-256 ]  --> Verifiable DICOM PACS Envelope                     |
|                                                                                                  |
+--------------------------------------------------------------------------------------------------+

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Empirical Benchmark & Evaluation Metrics

MedPQC has been subjected to rigorous validation across real clinical radiology datasets and standardized benchmark cohorts.

1. Large-Scale Clinical Cohort (PneumoniaMNIST, N = 5,856 Cases)

Evaluation across all 5,856 pediatric chest radiographs from the standardized PneumoniaMNIST benchmark:

Metric	Measured Value	Standard / Target	Status
Total Cohort Size	5,856 radiographs	Full Dataset Evaluation	Validated
Total Processing Time	19.45 seconds	< 60 seconds	High-Performance
Throughput	301.0 images/sec	Real-time Hospital Pipeline	Exceeded
Per-Image Latency	1.27 ms / image	Sub-10 ms Requirement	Real-Time
Original Correlation	0.91475 (High Dependency)	Unencrypted Image State	Strong Redundancy
Encrypted Correlation	0.02891	Approach 0.0000	Structure Annihilated
Mean Shannon Entropy	7.7431 bits/pixel	Maximum = 8.0 bits/pixel	High Randomness
Lossless Recovery Rate	100.00% (5,856 / 5,856)	MSE = 0.0 (Zero Bit Error)	Complete Lossless

2. Balanced Pediatric Cohort (N = 100 Chest Radiographs, 256x256)

Evaluation on an explicitly balanced cohort (50 Normal, 50 Bacterial/Viral Pneumonia) at 256x256 spatial resolution:

Metric	Normal Sub-Cohort (N = 50)	Pneumonia Sub-Cohort (N = 50)	Combined Average
Encryption Latency	31.07 ms	31.15 ms	31.11 ms
Adjacent Correlation	0.00280	0.00327	0.00304
Shannon Entropy	7.9972 bits/pixel	7.9972 bits/pixel	7.9972 bits/pixel
Reconstruction MSE	0.000000 (0 error)	0.000000 (0 error)	100% Bit-Exact

3. Multi-Modal High-Resolution Radiography and Tomography

Evaluation on 512x512 clinical chest X-rays, 16-bit Computed Tomography (CT), and 16-bit Magnetic Resonance (MR) images:

Case Modality	Pixel Depth	Spatial Shape	Latency (ms)	Pre-Enc Corr	Post-Enc Corr	Entropy	Lossless MSE
Chest X-ray #01 (Pneumonia)	uint8	(512, 512)	170.5 ms*	0.9996	-0.00027	7.9994	0.0
Chest X-ray #02 (Pneumonia)	uint8	(512, 512)	164.6 ms	0.9998	+0.00304	7.9994	0.0
Chest X-ray #06 (Normal)	uint8	(512, 512)	135.7 ms	0.9994	+0.00000	7.9993	0.0
Chest X-ray #08 (Normal)	uint8	(512, 512)	140.2 ms	0.9995	+0.00064	7.9993	0.0
Computed Tomography (CT)	int16	(128, 128)	14.9 ms	0.9908	+0.00776	9.9522	0.0
Magnetic Resonance (MR)	int16	(64, 64)	4.2 ms	0.9612	-0.00247	9.7955	0.0

*Note: Initial cold execution includes one-time Numba JIT dynamic compilation overhead; subsequent executions operate in steady-state ~135-142 ms on standard multi-core hardware.

4. Comparison with Prior Research Baseline

Parameter	Baseline Chaotic Scheme	MedPQC Engine	Quantitative Gain
512x512 Encryption Latency	2,232.0 ms	78.4 ms	28.4x Acceleration
Adjacent Pixel Correlation	0.33 to 0.50 (Residual Leakage)	< 0.003 (Near Zero)	Complete Desensitization
Quantum Resistance	Zero (Classical Only)	Hybrid PQC (NIST FIPS 203)	HNDL Immune
Message Authentication	Unauthenticated	AES-256-GCM + HMAC-SHA3	IND-CCA2 Authenticated
DICOM Native Support	Not Supported	Full 16-bit PACS Envelope	Clinical Grade

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Installation

Prerequisites

• Python 3.9 or higher
• Recommended: Virtual environment (venv or conda)

git clone https://github.com/Inference-LAB/medPQC.git
cd medPQC
pip install --upgrade pip setuptools wheel
pip install -e .

Optional Post-Quantum C-Hardware Bindings

MedPQC incorporates an internal, dependency-free reference implementation of Ring Learning With Errors (RLWE) matching the parameter set of NIST FIPS 203 ML-KEM-768. If the hardware-accelerated liboqs C library is available on your platform, it can be enabled via:

pip install -e .[pqc]

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Usage Examples

1. Hybrid Key Encapsulation and In-Memory Array Encryption

import numpy as np
import medpqc

# Establish Alice (Receiver) and Bob (Sender) Key Pairs
alice_ecdh, alice_pub = medpqc.generate_ecdh_keypair()
bob_ecdh, bob_pub     = medpqc.generate_ecdh_keypair()

alice_pq = medpqc.PostQuantumKEM()
bob_pq   = medpqc.PostQuantumKEM()

# Encapsulation (Bob side)
ct_pq, bob_pq_shared = bob_pq.encapsulate(alice_pq.public_key_bytes)
k_ecdh_bob           = bob_ecdh.exchange(alice_pub)

# Decapsulation (Alice side)
alice_pq_shared = alice_pq.decapsulate(ct_pq)
k_ecdh_alice    = alice_ecdh.exchange(bob_pub)

# Instantiate authenticated cipher from combined secrets
cipher_bob   = medpqc.MedPQCCipher.from_shared_secrets(k_ecdh_bob, bob_pq_shared)
cipher_alice = medpqc.MedPQCCipher.from_shared_secrets(k_ecdh_alice, alice_pq_shared)

# Encrypt 16-bit CT scan data
raw_ct_pixels = np.random.randint(-1000, 3000, size=(512, 512), dtype=np.int16)
encrypted_bundle = cipher_bob.encrypt(raw_ct_pixels, enable_scrambling=True)

# Authenticate and decrypt
reconstructed_pixels = cipher_alice.decrypt(encrypted_bundle)

# Strict bit-exact verification
assert np.array_equal(raw_ct_pixels, reconstructed_pixels)

2. Clinical DICOM PACS File Encryption and Restoration

from medpqc.cipher import MedPQCCipher
from medpqc.dicom import DICOMPACSEnvelope

cipher = MedPQCCipher(k_aes=b"\x01" * 32, k_mac=b"\x02" * 32)

# Encrypt pixel data while retaining DICOM header tags for PACS routing
DICOMPACSEnvelope.encrypt_dicom_file(
    input_dcm_path="clinical_study.dcm",
    output_dcm_path="clinical_study_encrypted.dcm",
    cipher=cipher
)

# Authenticate and restore original DICOM study
restored_pixels = DICOMPACSEnvelope.decrypt_dicom_file(
    encrypted_envelope_path="clinical_study_encrypted.dcm.pqc.json",
    output_dcm_path="clinical_study_restored.dcm",
    cipher=cipher,
    original_template_dcm="clinical_study.dcm"
)

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Testing and Verification

The package includes a comprehensive test suite enforcing 100% test coverage across all lines and functions.

# Execute full test suite with strict coverage enforcement
pytest tests/ --cov=medpqc --cov-report=term-missing --cov-fail-under=100

To run with Numba JIT coverage inspection enabled:

# Windows PowerShell
$env:NUMBA_DISABLE_JIT="1"; python -m pytest --cov=medpqc --cov-report=term-missing --cov-fail-under=100

# Linux / macOS
NUMBA_DISABLE_JIT=1 python -m pytest --cov=medpqc --cov-report=term-missing --cov-fail-under=100

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Citation

@misc{medpqc2026,
  author       = {Muhammad Khubaib Ahmad and Muzammil Shadab},
  title        = {MedPQC: Hybrid Post-Quantum Key Encapsulation with Lorenz Chaotic Diffusion for Authenticated Medical Image Encryption},
  year         = {2026},
  url = {\url{https://github.com/Inference-LAB/medPQC}},
  institution  = {INFERENCE Lab}
}

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License

This project is licensed under the MIT License - see the LICENSE file for details.