Title Page

Abstract

Acronyms & Abbreviations

Contents

Chapter 01. Introduction 18

1.1. Background & Motivation 18

1.2. Problem Statements 20

1.2.1. Harnessing Quantumness for Information Exchange: Challenges and Solutions 20

1.2.2. Strengthening Classical Information Exchange: Beyond Classical Cryptography 20

1.2.3. Future-Proofing Blockchain: Quantum-Resistant Cryptographic Solutions 21

1.3. Main Contributions 22

1.3.1. Quantum States for Classical Data 22

1.3.2. Nonlinear Confusion Component on the Bounded Points of Quantum States 23

1.3.3. Security and Privacy of Blockchain using Blind Quantum Computation 23

1.4. Thesis Organization 24

Chapter 02. Probabilistic Model of Quantum States for Classical Data Security 26

2.1. Introduction 26

2.2. Methodology 30

2.2.1. Generation of quantum spin states 30

2.2.2. AQS scheme 34

2.2.3. Proposed model for state transfer 37

2.3. Experimental results 41

2.4. Discussion 43

2.4.1. Attacks on model 44

2.4.2. Attacks on AQS 47

2.4.3. Characteristics comparison 49

2.5. Applications 52

2.5.1. Satellite imagery 52

2.5.2. Quantum internet 52

2.5.3. Internet of things security 52

Chapter 03. Design of Highly Nonlinear Confusion Component Based on Entangled Points of Quantum Spin States 54

3.1. Introduction 54

3.1.1. Problem statement 56

3.1.2. Related work 56

3.1.3. Contribution 58

3.2. Methodology 59

3.2.1. Evaluation of Quantum dots 60

3.2.2. Generation of balanced Boolean function values 62

3.2.3. Algorithm 67

3.2.4. Structural flowchart 69

3.3. Experimental results 69

3.3.1. Generated S-boxes 71

3.3.2. Nonlinearity comparison 73

3.3.3. SAC and BIC comparison 74

3.3.4. NIST statistical analyses 74

3.3.5. Balancedness, Bijectivity, LP, and DP comparison 76

3.3.6. Cryptanalytic analyses comparison 78

3.4. Discussion 78

Chapter 04. QuChain: On the Security and Privacy of Peer-to-Peer System using Blind Quantum Computation 82

4.1. Introduction 82

4.2. Quantum information processing and the blockchain technology 85

4.2.1. Quantum information 86

4.2.2. Quantum blockchain 87

4.3. Measurement-based BQC for peer-to-peer classical data processing 89

4.3.1. Quantum computation for classical data processing 90

4.3.2. BQC for classical P2P system 92

4.4. Discussion 95

Chapter 05. Conclusion and Future Directions 98

Appendices 100

Appendix Ⅰ 100

1.1. Experimental results 100

Appendix Ⅱ 110

2.1. Fundamental terminologies 110

2.2. Evaluation criteria for s-boxes 111

Publications 119

Frontiers of Physics (SCIE) 119

Scientific Reports (SCIE) 119

IEEE Conference on Nanotechnology 119

References 126

Table 1. Similarity analysis of original and recovered surveillance drone imagery. 43

Table 2. Comparison of the proposed probabilistic model with existing methodologies. 47

Table 3. Comparison of the proposed scheme with existing methodologies. 51

Table 4. Algorithm for designing of S-box 67

Table 5. Evaluated S-box 'S₁' with the aforementioned methodology. 72

Table 6. Evaluated S-box 'S₂' with the aforementioned methodology. 72

Table 7. Evaluation of nonlinearities for generated S-boxes and comparison with benchmark approaches. 73

Table 8. Evaluation of SAC and BIC for generated S-boxes and comparison with benchmark approaches. 75

Table 9. Evaluation of NIST statistical test suite on the generated S-boxes and comparison with benchmark approaches. 76

Table 10. Evaluation of balancedness., bijectivity, LP, and DP for generated S-boxes and comparison with benchmark approaches. 77

Table 11. Cryptanalyses scrutinization of the generated S-boxes and comparison with benchmark approaches. 79

Table 12. Comparative analysis of recent studies in QC and QB 89

Table 13. Pixel correlation coefficient analysis for the original and the recovered images. 108

Table 14. Similarity analyses between the original and recovered images. 109

Figure 1. Quantum Supremacy - threatens the complexity of traditional cryptography techniques. 19

Figure 2. Quantum-Safe Migration 19

Figure 3. Demonstration of a six-point spin state system (domain of -21.104 to 9.328 with a step size of 5.558) for a solo qubit. 33

Figure 4. Mechanism for classical data sharing upon the transition of unclonable quantum states 38

Figure 5. (a) Probabilistic version of states for classical data, and (b) measurement of the basis for finding the states. 38

Figure 6. Proposed methodology for secure data sharing between two entities on the conjunction of quantum states. 40

Figure 7. Experimental analysis of classical drone imagery transition into quantum states and imagery recovery from the states upon reception based on measurement of the spin lock system. 42

Figure 8. (a) Evaluation of quantum dots at the entangled point of spin states. (a) Extraction of dot points at the 8th entangled state in the phase domain of 0 to 360 with a step size of 90 63

Figure 8. (b) Evaluation of quantum dots at the entangled point of spin states. (b) Extraction of dot points at the 14th entangled state in the phase domain of 0 to 360 with a step size of 90 64

Figure 8. (c) Evaluation of quantum dots at the entangled point of spin states. (c) Extraction of dot points at the 1st entangled state in the phase domain of -90 to 90 with a step size of 20. 65

Figure 9. Demonstration of Quantum dots in entangled states to produce binary numbers and their decimal values for the confusion component. 66

Figure 10. Possible Boolean functions for the mapping of 4 bits to a 1-bit value. 66

Figure 11. Flowchart to extract the highly nonlinear confusion component(s). 70

Figure 12. Reckonings of a single qubit in form of states 87

Figure 13. Reckonings of single qubit to form spin states at different phases. (a) Spin of states around X-axis, (b) Spin of states around Y-axis. 90

Figure 14. Classical blockchain system with a full-fledged quantum server. 94

Figure 15. Demonstration of a 15-point spin state system (domain of 85.1176 to 159.8238 with a step size of 5.0891) for a solo qubit. 102

Figure 16. Demonstration of a 25-point spin state system (domain of -60 to 60.8238 with a step size of 5.0091) for a solo qubit. 103

Figure 17. Pixel correlation analysis of original and recovered multispectral images: (a-d) the original image and correlation analysis in the horizontal,... 105

Figure 18. Pixel correlation analysis for original and recovered abdominal MRI images: (a-d) the original image and correlation analysis in the... 106

Figure 19. Pixel correlation analysis for original and recovered abdominal Airplane images: (a-d) the original image and correlation analysis in the... 107

 The recent advancements in quantum information theory have greatly expanded the capability to simulate state superpositions, providing quantum algorithms with an exponential speed advantage over classical counterparts. This development renders traditional and current cryptographic methods (both encryption and authentication) vulnerable to quantum computer algorithms like Shor's and Grover's. Advanced technology now allows for enhanced data security by encoding classical information into small, single-use quantum states through quantum-assisted classical computing. In light of frequent data breaches and strict privacy laws, this research introduces a combined quantum-classical approach for transforming classical data into unique, unreplicable states and demonstrates perfect state transfer to represent classical information. To reduce complexity in implementation, this thesis suggests a flexible quantum signature method that bypasses the need for establishing entangled states, thus simplifying user authentication for sending and receiving states for classical data retrieval. The results from the probabilistic model show that the quantum-assisted classical framework significantly improves the security and efficiency of digital data, leading towards practical applications.

Securing data transmission over vulnerable networks often involves cryptosystems. Substitution boxes play a crucial role in introducing confusion by nonlinearly mapping inputs to outputs. A block cipher's confusion component is deemed secure against cryptanalysis if it exhibits high nonlinearity and low probabilities for differential and linear approximations. This research focuses on creating a highly nonlinear substitution-permutation network based on quantum spin state blotch symmetry in the Galois field GF(28). The effectiveness of this methodology is assessed through various measures of performance, randomness, and cryptanalytics. The findings confirm that the developed nonlinear confusion components enhance block cipher effectiveness and provide superior cryptographic strength with a higher signal-to-noise ratio compared to existing techniques.

With the emergence of quantum computing, the security and trustworthiness of blockchain technology are increasingly at risk. Quantum advancements could compromise the cryptographic methods currently safeguarding blockchain systems. This thesis explores the impact of quantum computing as a threat to blockchain integrity and discusses the potential of blind quantum computation in countering these risks. The proposed blind quantum computation method for blockchain allows for the classical processing of encrypted data, thereby safeguarding records in a quantum-safe manner without revealing any information about the data itself.