💻 computer science

Quantum-Resilient DICOM Image Secret Sharing with Quasi-Periodic Unitary Scrambling and Hypergraph Authentication

This paper proposes AJIT, a high-fidelity classical–quantum hybrid framework that ensures quantum-resilient secure sharing and multiparty authentication of DICOM medical images by combining DTCWT-based compression, quasi-periodic unitary scrambling, and topological hypergraph verification to achieve lossless reconstruction and robust differential resistance.

Original authors: Digambar Padulkar, Jibi Abraham

Published 2026-07-10

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Digambar Padulkar, Jibi Abraham

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you have a super-sensitive medical photo, like an X-ray or an MRI, that holds a patient's most private secrets. Now, imagine you need to send this photo to a bunch of different doctors across the world, but you're terrified that a quantum computer (a super-fast, futuristic machine) might crack your code and steal the image.

This paper introduces a new, high-tech safety system called AJIT (Adaptive Joint-register Image Transformation). Think of AJIT as a magical, quantum-powered "secret recipe" for sharing medical images that is tough enough to withstand the power of future quantum computers.

Here is how the magic trick works, step-by-step:

1. The "Shrink Ray" (Compression)

First, the system takes a huge medical image (like a 128x128 pixel picture) and shrinks it down. It doesn't just squish it; it uses a special tool called DTCWT (Dual-Tree Complex Wavelet Transform).

The Analogy: Imagine a giant, detailed map. Instead of copying the whole thing, this tool cuts out the most important roads and landmarks while throwing away the empty fields.
The Result: This shrinks the image's "quantum footprint" by 75%. It keeps all the critical details (like tumors or fractures) perfectly clear but uses way less memory. The paper tested this against other methods like FFT and DCT, and found that DTCWT was the only one that kept the medical details sharp enough for doctors to use.

2. The "Quantum Shuffle" (Scrambling)

Once the image is shrunk, it's turned into a quantum state (a fancy way of saying it's made of tiny quantum bits). But just being quantum isn't enough; it needs to be scrambled so no one can guess what it is.

The Problem with Old Methods: Previous methods used "periodic" shuffles, like a Rubik's Cube. If you twist it enough times, it goes back to the start. Hackers could just keep twisting until the image reappeared.
The AJIT Solution: This paper argues against those predictable, repeating shuffles. Instead, AJIT uses a Quasi-Periodic Unitary Operator (a fancy name for a chaotic shuffler).
The Analogy: Instead of a Rubik's Cube that repeats, imagine a shuffler that uses a random, never-ending sequence of spins. It's like a kaleidoscope that never shows the same pattern twice. Because the pattern never repeats, a hacker can't just "wait it out" to see the original image.

3. The "Secret Club" (Sharing & Authentication)

Now, the scrambled image is cut into pieces (shares) and sent to different people. But here's the catch: you can't just ask for the pieces back. You have to prove you belong to the "Secret Club."

The Hypergraph: The paper uses something called a Quantum Hypergraph. Think of a normal graph as a line connecting two dots. A hypergraph is like a net that can connect many dots at once.
The Test: Before anyone gets the pieces back, they have to pass a "topological phase-locked" test. It's like a secret handshake that involves a group of people holding hands in a specific quantum pattern. If even one person in the group is a liar or a hacker, the quantum "handshake" breaks, and the system instantly knows who the cheater is. The paper says this method can deterministically identify dishonest participants.

4. The "Ghost Key" (Teleportation)

Once the right group of doctors proves they are legitimate, they need the "key" to unscramble the image. But sending the key over the internet is dangerous because hackers might steal it.

The Solution: The paper uses Quantum Gate Teleportation.
The Analogy: Instead of mailing the key (which could be stolen), they "teleport" the key's effect directly to the receiver. The key itself never exists in a form that can be read or copied by a hacker. It's like sending a message that only appears when the receiver is standing in the right spot, and then vanishes instantly.

The Results (The "Did it work?" Check)

The authors didn't just dream this up; they ran simulations on a computer (using IBM's Qiskit simulator) to see if it held up. They tested it on 128x128 DICOM images (a standard medical image size).

Security: The system was incredibly good at hiding changes. If you changed just one tiny pixel in the original image, the scrambled version changed by 99.8157% (a metric called NPCR). This means a hacker can't guess the image by looking at small differences.
Quality: When the authorized doctors put the pieces back together, the image was almost perfect. The "Peak Signal-to-Noise Ratio" (PSNR) was 58.48 dB, and the "Structural Similarity" (SSIM) was above 0.99. In plain English: the reconstructed image looked almost exactly like the original, with no blurry spots or lost details.
Randomness: The "shares" (the pieces sent to the doctors) looked like pure static noise, with an entropy of 7.70. This means a hacker looking at a single piece would see absolutely nothing useful.

What This Paper Does Not Say

It's important to know what this paper doesn't claim.

No Real Quantum Computers Yet: The authors explicitly state these results are from simulations (running on a powerful computer that pretends to be a quantum machine). They have not yet run this on a physical quantum computer in a real hospital.
No "Magic" Cures: This is a security tool, not a medical diagnosis tool. It doesn't find tumors; it just keeps the X-ray safe while it travels.
No Future Guarantees: The paper suggests this is a strong foundation for the future, but it doesn't claim the problem is "solved" for all time. It's a proposed framework that needs more testing on real hardware.

In short, AJIT is a clever, multi-layered security system that shrinks medical images, scrambles them with a never-repeating pattern, splits them into noise-like pieces, and only lets the right group of people put them back together using a "ghost key" that can't be stolen. It's a promising shield for the future of digital healthcare, at least according to these computer simulations.

Technical Summary: Quantum-Resilient DICOM Image Secret Sharing with Quasi-Periodic Unitary Scrambling and Hypergraph Authentication

Problem Statement
The rapid digitization of healthcare infrastructure has created an urgent need for secure medical image exchange, particularly as emerging quantum computing threats (e.g., Shor's and Grover's algorithms) compromise classical cryptographic assumptions. Existing Quantum Secret Sharing (QSS) schemes for medical images face three critical limitations:

Periodicity Vulnerabilities: Many rely on periodic scrambling operators (e.g., Arnold transforms) with finite cycles, making them susceptible to cycle-detection and statistical cryptanalytic attacks.
Resource Overhead: Direct encoding of high-resolution DICOM images into quantum states incurs prohibitive qubit requirements, rendering them impractical for current Noisy Intermediate-Scale Quantum (NISQ) devices.
Authentication Gaps: Participant authentication is often treated separately from the secret-sharing process, leaving systems vulnerable to dishonest participants and unauthorized reconstruction.

Furthermore, medical images demand lossless structural preservation; even minor distortions can compromise clinical diagnosis, necessitating a framework that balances high-fidelity compression with robust security.

Methodology: The AJIT Framework
The authors propose AJIT (Adaptive Joint-register Image Transformation), a classical–quantum hybrid framework designed for secure medical image secret sharing and multiparty authentication. The methodology proceeds through the following stages:

Compression via DTCWT:
- To reduce the quantum resource footprint, the framework applies a Dual-Tree Complex Wavelet Transform (DTCWT) to the input DICOM image.
- This decomposition yields one approximation subband and six directional detail subbands ( $\pm15^\circ, \pm45^\circ, \pm75^\circ$ ).
- By utilizing only the approximation subband for the primary quantum state, the framework achieves a 75% reduction in Hilbert space complexity (reducing positional register qubits by two for a $2^n \times 2^n$ image) while preserving essential anatomical features.
- The coefficients are encoded using Q8.8 fixed-point representation to ensure lossless reconstruction of floating-point subband data.
Quantum Representation (NEQR):
- The compressed approximation subband is encoded into a quantum state using the Novel Enhanced Quantum Representation (NEQR). Unlike probabilistic representations (e.g., FRQI), NEQR stores grayscale values in computational basis states, enabling deterministic, bit-perfect recovery of diagnostic details.
Quasi-Periodic Scrambling ( $U_{AJIT}$ ):
- A bespoke global unitary operator, $U_{AJIT} = U_{conf} \circ U_{diff}$ , is applied to scramble the quantum state.
- Diffusion Layer ( $U_{diff}$ ): Utilizes a Random Circuit Ansatz with stochastic qubit rotations ( $R_y(\theta_i), R_z(\phi_i)$ ) and an entanglement ladder (CNOT gates) to disperse spatial correlations.
- Confusion Layer ( $U_{conf}$ ): Implements a Cipher-State Feedback (CSF) mechanism with a circular bit-rotation operator ( $\Gamma_L$ ). The shift parameter $L$ is dynamically derived from the rotation angles and constrained to prime numbers to ensure maximal avalanche effects.
- Key Innovation: Unlike periodic operators, $U_{AJIT}$ possesses an incommensurate eigenphase spectrum, rendering the scrambling effectively non-repeating within any operational timeframe and resistant to periodicity-based attacks.
Secret Sharing via Quantum Manifold Slicing (QMS):
- The scrambled quantum manifold is distributed into $n$ statistically decorrelated shares using a Quantum Manifold Slicing (QMS) operator.
- This employs a $(k, n)$ threshold scheme where shares are generated via XOR operations with orthogonal masks. The process is lossless and free from the Galois field limitations found in classical polynomial-based schemes (e.g., Shamir's).
Hypergraph Authentication:
- Prior to reconstruction, participant legitimacy is verified using a Quantum Hypergraph (QH) authentication protocol.
- This layer utilizes a topological phase-locked mechanism where authorized groups (hyperedges) satisfy specific stabilizer syndromes.
- Dishonest Participant Detection: The system employs Stabilizer-Syndrome Detection via an ancilla-assisted Hadamard test. If a participant applies a unitary error (cheating), the stabilizer condition fails, deterministically identifying the malicious actor and aborting the protocol.
Secure Operator Delivery via Gate Teleportation:
- The inverse operator $U_{AJIT}^\dagger$ required for decryption is never transmitted classically.
- Instead, it is delivered via port-based quantum gate teleportation grounded in the Choi–Jamiolkowski isomorphism. This ensures the decryption operator remains in a quantum state, protected by the no-cloning theorem, and is only applied by authorized recipients.

Key Contributions
The paper claims the following principal contributions:

Quasi-Periodic Unitary: A novel scrambling operator $U_{AJIT}$ with an incommensurate eigenphase spectrum that eliminates finite-period cycles.
Integrated Key Manifold: A Cryptographic Key Manifold ( $K_k$ ) derived directly from DTCWT rotation angles, coupling compression and cryptography without a separate key distribution channel.
Lossless QMS: A $(k, n)$ Quantum Manifold Slicing operator that avoids Galois field limitations, ensuring perfect reconstruction.
Hypergraph Authentication: A topological phase-locked authentication protocol that deterministically identifies dishonest participants via stabilizer syndrome detection.
Enhanced NEQR: An encoding scheme using Q8.8 fixed-point representation for lossless floating-point subband handling.
Secure Teleportation: A port-based gate teleportation protocol that delivers the decryption operator without classical exposure.

Experimental Results
Numerical simulations were conducted on 128 $\times$ 128 DICOM images using the IBM Quantum Aer Simulator and Qniverse. The results demonstrate:

Image Quality: The reconstructed images achieved an average PSNR of 58.48 dB and SSIM > 0.99, confirming near-lossless diagnostic integrity.
Security Metrics:
- NPCR (Number of Pixels Change Rate): Average of 99.8157%, indicating strong resistance to differential attacks.
- UACI (Unified Average Changing Intensity): Average of 33.5423%, consistent with secure cipher expectations.
- Entropy: Shares exhibited an entropy of $H \approx 7.70$ , confirming high randomness and lack of information leakage.
Compression: The DTCWT stage successfully reduced the image size to a $64 \times 64$ approximation subband, saving approximately two qubits in the positional register.

Significance and Claims
The authors assert that AJIT provides a comprehensive solution for decentralized telemedicine environments facing quantum threats. By integrating compression, quasi-periodic scrambling, and hypergraph-based authentication, the framework addresses the specific constraints of medical imaging (lossless fidelity) and current quantum hardware limitations (qubit scarcity). The use of gate teleportation for operator delivery and stabilizer-based authentication offers a robust defense against both external eavesdropping and internal dishonest participants, establishing a scalable, quantum-resilient architecture for secure Electronic Health Record (EHR) management.