🔐 Quantum Encryption Scheme Based on Taylor Series & Fourier Transform

Published in IEEE | Amrita Vishwa Vidyapeetham, Coimbatore

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📄 Abstract

This paper proposes a novel quantum encryption scheme combining Quantum Fourier Transform (QFT), Taylor Series, and quantum gates to establish a secure, key-based encryption and decryption pipeline. The scheme is designed to enable privacy-preserving machine learning and federated learning by performing computations directly on encrypted data using CKKS-based Homomorphic Encryption.

The proposed approach achieves identical accuracy on encrypted vs plaintext inference — 96.60% accuracy on a 2000-sample diabetes dataset — demonstrating that secure computation does not compromise model performance.

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🏗️ System Architecture

Classical Data
      │
      ▼
Ry Gates (encode data into quantum states)
      │
      ▼
Quantum Fourier Transform (QFT) — domain transformation
      │
      ▼
Rz Gates (public key — Euler phase shifts)
      │
      ▼
Rx Gates (secret signal embedding from Taylor series)
      │
      ▼
Encrypted Quantum State → Measurement (1024 shots)
      │
      ▼
Inverse QFT + Remove Taylor signal → Decrypted State

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📁 Repository Structure

Quantum-Encryption-QFT-Taylor/
├── README.md
├── requirements.txt
├── src/
│   ├── ckks_encryption.py       # CKKS scheme with TenSEAL
│   ├── quantum_circuit.py       # QFT + gate-based encryption circuit
│   ├── taylor_keygen.py         # Taylor series private key generation
│   ├── homomorphic_inference.py # Encrypted model inference
│   └── evaluate.py              # Accuracy comparison: plaintext vs encrypted
├── notebooks/
│   └── Quantum_Encryption_Demo.ipynb
├── results/
│   ├── encrypted_state_distribution.png
│   ├── decrypted_state_distribution.png
│   └── classification_report.txt
├── images/
│   └── quantum_circuit_diagram.png
└── LICENSE

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⚙️ Methods

1. CKKS Homomorphic Encryption

Parameter	Value
Scheme	CKKS (Cheon-Kim-Kim-Song)
Poly Modulus Degree	8192
Coeff Mod Bit Sizes	[60, 40, 40, 60]
Global Scale	2^40
Library	TenSEAL (Python)

• Supports approximate arithmetic on encrypted real-valued data
• Galois keys generated for rotation operations
• Plaintext → polynomial encoding → encryption → homomorphic ops → decrypt

2. Proposed Quantum Encryption Scheme

Component	Role
Ry Gates	Encode classical data into quantum states
QFT	Transform data into frequency domain
Rz Gates	Apply public key (Euler phase shifts)
Rx Gates	Embed Taylor series secret signal
Measurement	1024 shots over basis states {

3. Taylor Series Key Generation

The private key is derived from a Taylor expansion:

f(x) = Σ (f^n(a)/n!) * (x-a)^n

The function f and expansion terms are known only to the key holder. The generated signal is added to data before QFT transformation.

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📊 Results

CKKS Encrypted Inference — Diabetes Dataset

Metric	Plaintext	Encrypted
Accuracy (100 samples)	97.00%	97.00%
Accuracy (2000 samples)	96.60%	96.60%

Zero accuracy loss under homomorphic encryption — privacy-preserving inference confirmed.

Classification Report (Logistic Regression on Encrypted Data)

Class	Precision	Recall	F1-Score	Support
0	0.85	0.79	0.82	192
1	0.98	0.99	0.98	1808

Quantum State Measurement (1024 shots)

Quantum State	Decrypted	Encrypted
|00⟩	277	246
|01⟩	251	255
|10⟩	236	246
|11⟩	260	277

Near-uniform distributions confirm successful encryption. Decrypted distribution recovers original state.

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🚀 Getting Started

pip install -r requirements.txt

Run CKKS Encrypted Inference

python src/homomorphic_inference.py --dataset diabetes

Run Quantum Circuit Demo

python src/quantum_circuit.py --shots 1024

Evaluate Plaintext vs Encrypted Accuracy

python src/evaluate.py

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📦 Requirements

tenseal==0.3.14
qiskit==0.44.1
numpy==1.24.3
scikit-learn==1.3.0
pandas==2.0.3
matplotlib==3.7.2

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👥 Authors

Name	Roll No.
Hari Sudharsan G	CB.AI.U4AIM24113
Nithin S	CB.AI.U4AIM24133
Amirthavarshini B	CB.AI.U4AIM24154
Devadharshini M	CB.AI.U4AIM24126

Institution: Amrita Vishwa Vidyapeetham, Coimbatore

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📚 Citation

@inproceedings{harisudharsan2024quantum,
  title     = {Quantum Encryption Scheme based on Taylor Series and Fourier Transform},
  author    = {Hari Sudharsan, G. and Nithin, S. and Amirthavarshini, B. and Devadharshini, M.},
  booktitle = {IEEE},
  year      = {2024},
  institution = {Amrita Vishwa Vidyapeetham, Coimbatore}
}

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📜 References

1. Hong, C. Recent advances of privacy-preserving ML based on Homomorphic Encryption. Security and Safety, 2025.
2. Dutta et al. Federated Learning with Quantum Computing and FHE. arXiv:2409.11430, 2024.
3. Patel, M. Diabetes prediction dataset. Kaggle, 2025.

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📍 Amrita Vishwa Vidyapeetham, Coimbatore, Tamil Nadu  |  Published in IEEE