ENHANCEMENT OF REVERSIBLE IMAGE STEGANOGRAPHY AND OPTIMIZATION OF QUANTUM IMAGE REPRESENTATION USING THE NEQR MODEL

Abstract

Reversible steganography allows for exact reconstruction of the cover media after hidden data extraction, making it vital for applications such as content authentication, medical imaging, and military communications. Various reversible steganography techniques include histogram shifting, image interpolation, and difference expansion. Histogram shifting methods apply shifting to pixel-domain histograms or prediction error histograms. Prediction error histogram methods offer higher embedding capacity, but they are more complex, lack a guaranteed lower bound on PSNR, and are more susceptible to histogram-based steganalysis. Pixel-domain histogram shifting techniques, though simpler and more efficient with a theoretical PSNR bound, generally have lower embedding capacity. Under this project, experiments are conducted on pixel-domain histogram shifting- based techniques. The capacity and histogram for varying number of non-overlapping image blocks and histogram blocks are analyzed. Experimental results show that embedding in image blocks does not significantly enhance the capacity compared to embedding in histogram blocks. Analysis of histogram blocks shows that embedding in two blocks yields the optimal results. A method is developed for making histogram shifting adaptive to payload size and a two layer embedding is developed for improved hiding capacity. Compared to previous methods, the two-layer embedding achieves higher capacity, better resistance to steganalysis, and maintains the PSNR acceptable for real-world applications. Quantum computing is an advancing field that offers significant speed advantages for certain computational tasks over classical computing. Notable examples include Shor’s algorithm, which efficiently solves integer factorization and discrete logarithm problems, and Grover’s algorithm, which accelerates the search process in unstructured databases. Quantum computing is based on quantum arithmetic operations where addition forms the core of all operations, as subtraction, multiplication, exponentiation, and division ix can all be reduced to repeated or modified forms of addition. Experiments are conducted for performance analysis of quantum addition on quantum hardware. Development of quantum circuits for addition and comparison, including half adders, full adders, Toffoli-based adders, QFT-based adders (utilizing the Quantum Fourier Transform), and quantum comparators is carried out using IBM Qiskit. The circuits are first validated on ideal simulators to confirm correctness, followed by testing on noisy simulators to emulate real quantum hardware conditions. Final execution is carried out on IBM's Eagle 127-qubit Quantum Processing Unit (QPU). Results show that computation accuracy on actual hardware is limited by physical constraints such as short qubit coherence times and instability. A performance comparison shows that Toffoli-based adders outperform QFT-based adders in terms of accuracy, making them more reliable for precise arithmetic computations. Quantum image representation provides exponential efficiency in image storage and processing. It relies on the fundamental principles of superposition and entanglement. NEQR (Novel Enhanced Quantum Representation) is a lossless encoding method used to represent digital images on a quantum computer. It is widely applicable in domains such as quantum machine learning, image steganography, and quantum image analysis. This work introduces two enhancements to the NEQR framework: (1) Optimizing the decomposition of Multi-Controlled NOT (MCX) gates into Toffoli gates, and (2) Parallelizing the NEQR by parallel bit-plane encoding of the NEQR circuit, where the NEQR circuit is simultaneously constructed for each of the eight bit-planes of an image, thereby reducing overall circuit depth. Experimental results demonstrate that these enhancements lead to reduced circuit depth and faster execution, thereby mitigating decoherence-related errors. Additionally, quantum image processing operations that demonstrate exponential speedup over classical approaches — such as image negation, rotation, and intensity superposition — are also implemented and evaluated as part of this work.