Abstract:

Cryptography is the practice and study of techniques for securing information and communication through codes, ensuring that only authorized individuals can access the original data. Properties of chaotic dynamical systems such as sensitive dependence on initial conditions and random-like behavior share unique characteristics with cryptographic primitives, which allow chaotic systems to be applied to cryptography. Because image data has high redundancy and strong correlation between adjacent pixels, traditional block ciphers are not suitable for encrypting real-time image data. Therefore, designing cryptographic algorithms based on the information content of the image is crucial for secure communication, offering enhanced security, accuracy, and efficiency.  Over the past two decades, many integer-order chaotic systems have been used to design secure image encryption algorithms. The fractional-order chaotic dynamical systems exhibit higher nonlinearity and degrees of freedom with respect to fractional derivative orders, and generate more complex random sequences than integer-order chaotic systems. In this work, we propose image cryptosystems using fractional-order chaotic system. Quantum image processing is an emerging technology that uses the laws of quantum mechanics to efficiently perform various classical image processing tasks. Its research focuses on two key directions: 1) developing quantum image representation (QIR) methods, and 2) designing resource-efficient quantum circuits for implementing complex image processing operations. The QIR methods encode classical image information consisting of  pixels into a normalized quantum state of  quantum bits. In this work, we analyze several existing QIR methods and propose an improved color-encoding mapping that significantly improves the performance of these QIR methods. Arithmetic in finite fields with characteristic 2 is fundamental to many cryptographic algorithms. By using the normal basis representation for elements of these fields, we design quantum circuits that efficiently perform addition, multiplication, exponentiation, and inversion operations. The proposed quantum circuits for exponentiation and inversion use fewer quantum resources compared to existing implementations. Additionally, we integrate linear, affine, and nonlinear transformations over finite fields of characteristic 2 with secure keys generated from fractional-order chaotic systems and propose six quantum image cryptosystems. Results of various experimental measures and performance analyses such as key space, histogram, visual effects, correlation, computational complexity, etc., verify that the proposed quantum image cryptosystems are fast, robust, and reliable.

Committee Members:

1. Dr. Nauman Raza (External Examiner, Associate Professor, Mathematics, Punjab University)

2. Dr. Ijaz Naqvi (Examiner, Associate Professor, EE, LUMS)

3. Dr. Reza Abdolmaleki (Examiner, Assistant Professor, Mathematics, LUMS)

4. Dr. Amer Rasheed (Supervisor, Former Associate Professor, Mathematics, LUMS)

5. Dr. Sultan Sial (Supervisor, Associate Professor, Mathematics, LUMS)

List of Publications:

1. M. Khan, A. Rasheed, Permutation-based special linear transforms with application in quantum image encryption algorithm, Quantum Information Processing, 18 (10) (2019) 1–21. https://doi.org/10.1007/s11128-019-2410-7.
2. M. Khan, A. Rasheed, A fast quantum image encryption algorithm based on affine transform and fractional-order Lorenz-like chaotic dynamical system, Quantum Information Processing, 21 (4) (2022). https://doi.org/10.1007/s11128-022-03474-0.
3. M. Khan, A. Rasheed, A secure controlled quantum image steganography scheme based on the multi-channel effective quantum image representation model, Quantum Information Processing, 22 (268) (2023). https://doi.org/10.1007/s11128-023-04022-0.
4. M. Khan, A. Rasheed, A high-capacity and robust steganography algorithm for quantum images, Chinese Journal of Physics, 85 (2023). https://doi.org/10.1016/j.cjph.2023.06.016.
5. M. Khan, A. Rasheed, A novel quantum image steganography scheme and improved method for encoding the color information of classical images into quantum states, Optical and Quantum Electronics, under review.
6. M. Khan, A. Rasheed, A lightweight secure quantum image encryption algorithm based on strong cryptographic keys, Optik, under review.