- Page 1: some results on Cryptanalysis of RS
- Page 5 and 6: Abstract In this thesis, we propose
- Page 7: Acknowledgements There are many peo
- Page 12 and 13: 2.3.7 Small Decryption Exponent Att
- Page 14 and 15: 7.4 The General Solution for EPACDP
- Page 17 and 18: List of Figures 1.1 Communication o
- Page 19 and 20: Chapter 1: Introduction 2 The motiv
- Page 21 and 22: Chapter 1: Introduction 4 there is
- Page 23 and 24: Chapter 1: Introduction 6 Discrete
- Page 25 and 26: Chapter 1: Introduction 8 Chapter 5
- Page 28 and 29: Chapter 2 Mathematical Preliminarie
- Page 30 and 31: 13 2.2 RSA Cryptosystem are impleme
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- Page 40 and 41: 23 2.3 Cryptanalysis of RSA to be h
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- Page 44 and 45: 27 2.4 Lattice and LLL Algorithm No
- Page 46 and 47: 29 2.4 Lattice and LLL Algorithm Wh
- Page 48 and 49: 31 2.5 Solving Modular Polynomials
- Page 50 and 51: 33 2.5 Solving Modular Polynomials
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- Page 54 and 55: 37 2.5 Solving Modular Polynomials
- Page 56 and 57: 39 2.6 Solving Integer Polynomials
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41 2.6 Solving Integer Polynomials
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43 2.7 Analysis of the Root Finding
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45 2.9 Conclusion 2.9 Conclusion No
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Chapter 3: A class of Weak Encrypti
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Chapter 3: A class of Weak Encrypti
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Chapter 3: A class of Weak Encrypti
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Chapter 3: A class of Weak Encrypti
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Chapter 3: A class of Weak Encrypti
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Chapter 3: A class of Weak Encrypti
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Chapter 3: A class of Weak Encrypti
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Chapter 3: A class of Weak Encrypti
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Chapter 4: Cryptanalysis of RSA wit
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Chapter 4: Cryptanalysis of RSA wit
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Chapter 4: Cryptanalysis of RSA wit
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Chapter 4: Cryptanalysis of RSA wit
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Chapter 4: Cryptanalysis of RSA wit
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Chapter 5 Reconstruction of Primes
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77 5.1 LSB Case: Combinatorial Anal
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79 5.1 LSB Case: Combinatorial Anal
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81 5.1 LSB Case: Combinatorial Anal
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83 5.1 LSB Case: Combinatorial Anal
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85 5.2 LSB Case: Lattice Based Tech
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87 5.3 MSB Case: Our Method and its
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89 5.3 MSB Case: Our Method and its
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91 5.3 MSB Case: Our Method and its
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93 5.3 MSB Case: Our Method and its
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Chapter 6 Implicit Factorization In
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97 6.1 Implicit Factoring of Two La
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99 6.1 Implicit Factoring of Two La
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101 6.1 Implicit Factoring of Two L
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103 6.1 Implicit Factoring of Two L
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105 6.1 Implicit Factoring of Two L
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107 6.2 Two Primes with Shared Cont
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109 6.2 Two Primes with Shared Cont
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111 6.3 Exposing a Few MSBs of One
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113 6.3 Exposing a Few MSBs of One
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Chapter 7 Approximate Integer Commo
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117 7.1 Finding q −1 mod p ≡ Fa
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119 7.2 Finding Smooth Integers in
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121 7.3 Extension of Approximate Co
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123 7.4 The General Solution for EP
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125 7.4 The General Solution for EP
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127 7.4 The General Solution for EP
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129 7.4 The General Solution for EP
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131 7.4 The General Solution for EP
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133 7.5 Sublattice and Generalized
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135 7.5 Sublattice and Generalized
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137 7.5 Sublattice and Generalized
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139 7.6 Improved Results for Larger
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141 7.6 Improved Results for Larger
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143 7.7 EGACDP The approach in this
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145 7.7 EGACDP Sinceinthiscasethema
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147 7.8 Conclusion poly{loga,k}. Th
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Chapter 8: Conclusion 150 Chapter 3
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Chapter 8: Conclusion 152 p 1 ,p 2
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Chapter 8: Conclusion 154 represent
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Chapter 8: Conclusion 156 Final Wor
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BIBLIOGRAPHY 158 [9] J. Blömer and
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BIBLIOGRAPHY 160 [31] B. de Weger.
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BIBLIOGRAPHY 162 [54] M.J.Hinek. Cr
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BIBLIOGRAPHY 164 [76] A. K. Lenstra
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BIBLIOGRAPHY 166 [97] A. Nitaj. Cry
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BIBLIOGRAPHY 168 [121] C. L. Siegel