Copyright
IIT Kharagpur
Contents
Title Page i
Declaration v
Certificate of Approval vii
Certificate ix
Table of Contents xiii
List of Figures xvii
List of Tables xix
List of Abbreviations xxi
1 Introduction 1
1.1 Objective and Scope of the Present Work. . . 1 1.2 Major Contributions of the Present Work . . . 3 1.3 Outline of the Thesis . . . 4
2 Background and Literature Survey 7
2.1 Error Control Code . . . 7 2.1.1 Reed Solomon Code . . . 8 2.2 Cellular Automata. . . 11
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CONTENTS
2.2.1 CA-based Byte Error Correcting Code . . . 15
2.3 Cryptography . . . 15
2.3.1 Block Cipher . . . 16
2.3.2 Stream Cipher . . . 24
2.3.3 Message Authentication Code . . . 25
2.3.4 Cryptographic Boolean Function . . . 27
2.4 Conclusions . . . 33
3 Family of Nonlinear Reversible Boolean Functions 35 3.1 Nmix . . . 37
3.1.1 Properties of Nmix . . . 38
3.1.2 Cryptographic Performance of Nmix . . . 40
3.2 Smix . . . 47
3.2.1 Properties of Smix: . . . 48
3.2.2 Cryptographic Performance of Smix . . . 50
3.2.3 Smix to Strengthen the Security of NLS . . . 54
3.3 Nimix . . . 63
3.3.1 Properties of Nimix . . . 64
3.3.2 Performance of Nimix . . . 65
3.3.3 Performance Comparison and Application . . . 68
3.4 Comparison of Three Proposed Functions . . . 72
3.5 Conclusions . . . 73
4 Cellular Automata Based Byte Error Correcting Code 75 4.1 Existing CA-Based Byte Error Correcting Code . . . 77
4.1.1 Weaknesses and Limitation. . . 78
4.2 Improved Byte Error Correcting Code . . . 81
4.2.1 Single Byte Error Correcting Code. . . 83
4.2.2 Double Byte Error Correcting Code . . . 84 xiv
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CONTENTS
4.3 Extension of the Scheme for 3 and 4 Bytes ECC . . . 96
4.3.1 3-byte Error Correcting Code . . . 96
4.3.2 4-byte Error Correcting Code . . . 104
4.4 8-bit CA Rule Vectors for all Primitive Polynomials . . . 106
4.5 Conclusions . . . 106
5 Block Cipher HDNM8 109 5.1 Diffusion Layer Using CA-based MDS code . . . 113
5.1.1 Superiority of the Proposed Diffusion Over AES-like Diffusion . . 116
5.2 Nonlinear Mixing Function: Bidnmix. . . 119
5.3 AES Substitution Box . . . 121
5.4 Design and Implementation of HDNM8 . . . 125
5.4.1 Hardware Implementation . . . 126
5.5 Security Analysis of HDNM8 . . . 131
5.5.1 Expected Differential Probability Value for Characteristic . . . 131
5.5.2 Maximum Expected Probability for Linear Characteristic. . . 133
5.5.3 Higher Order Differential Cryptanalysis . . . 133
5.5.4 Interpolation Attack . . . 133
5.5.5 Algebraic Attack . . . 134
5.5.6 Integral Cryptanalysis . . . 134
5.6 Dependence Tests . . . 135
5.7 Conclusions . . . 137
6 An Integrated Scheme for Message Authentication and Error Correction 139 6.1 Overview of Lam et al.’s Scheme . . . 141
6.2 Proposed Integrated ECC-MAC . . . 142
6.2.1 ECC-MAC . . . 143
6.2.2 Sender and Receiver . . . 144
6.2.3 Logic for Using Nmix . . . 147 xv
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6.3 Security Analysis . . . 150
6.4 Evaluation of the Proposed Scheme . . . 151
6.4.1 Computational Cost . . . 151
6.4.2 Bit variance and Entropy Test . . . 152
6.5 Conclusions . . . 156
7 Summary and Future Work 157 7.1 Summary . . . 157
7.2 Future Work . . . 158
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