Novel Encryption and Secret Sharing Schemes for Digital and Quantum Images

Abstract

This thesis manifests the work done in proposing and designing novel algorithms for digital image encryption. Di erent chaotic maps and their ergodic properties are exploited in designing these algorithms. Additionally, concepts like compressed sensing and Integer Wavelet Transform are also harnessed in designing encryption protocols. In the latter part of the thesis, a substantial amount of work is done to design a quantum image encryption algorithm based on the quantum formulation of a discrete chaotic map. The application of quantum secret sharing schemes is also acknowledged by proposing one. Several experimental results are presented in the form of qualitative and quantitative evaluations to support the algorithms proposed in the thesis. Comparative analysis with some existing approaches is given to highlight the applicability and the virtue of the proposed algorithms. The treatise starts with a general introduction of the proposed work along with a brief motivation. A brief inspection and review of the existing techniques related to image encryption, both chaos and quantum-based, and quantum secret sharing, is summed up in the rst chapter. The subsequent chapter deals with proposing a cryptosystem based on Fractional-order nonlinear chaotic di erential system. The work includes solving the fractional system numerically by applying the Adams- Bashforth-Moulton method. The scheme is composed of a 3D Arnold cat map that synthesizes with the di usion proposed in the scheme. The scheme is made plaintext and key-sensitive by implementing a key-scheduling algorithm. The next algorithm is a lossy-encryption scheme based on the synthesis of the chaotic Baker map and symmetric attractor. The scheme utilizes the Multi-Resolution Singular Value Decomposition (MR-SVD) of the image to encrypt the low-frequency subbands in contrast to the entire image, thereby making it computationally e cient without compromising the security. Another scheme based on compressive sensing (CS) and a nonlinear exponential function is also proposed. The main motivation for designing this CS-based scheme is to reduce the transmission cost of the cipher and at the same time, guarantee security and acceptable reconstruction of the original image using a sparse recovery solver. The subsequent algorithm deals with extending the usual image ciphers into a non-conventional scheme culminating in the generation of a visually meaningful cipher image (VMCI). The scheme uses a reference image, Lifting Wavelet, and a pairing function to generate the VMCI. In addition to the conventional security aspects, the scheme also withstands against various steganographic attacks. The latter half of the thesis focuses on designing protocols for quantum image encryption (QIE) and quantum secret sharing (QSS). The premise of QIE is a quantum realization of a 3D-Baker map, that is implemented in accordance with a quantum di usion mechanism based on Generalized Gray Code (GGC) scrambling and fractional chaotic system. The proposed QSS scheme is a (n; n) scheme based on the entangled Bell and Greenberger Horne Zeilinger (GHZ) states to share and transmit a secret with image sharing applications. The thesis is concluded based on the work presented in the earlier chapters. As a continuum, a brief description of the scope for further study is also given.