Cryptanalysis of RSA Factorization - Library(ISI Kolkata) - Indian ...

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and support they provided throughout my stay at the Institute. I would like to thank my Didi (elder sister) for her love and support. Last but not the least, I am grateful to my Parents for their understanding, never ending blessings, faith and support in every step <strong>of</strong> my life. I love you Maa and Baba! iv
To Thaakuma (Grandmother), the first teacher in my life. v
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
Page 32 and 33: 15 2.2 RSA Cryptosystem • private
Page 34 and 35: 17 2.2 RSA Cryptosystem istic prima
Page 36 and 37: 19 2.2 RSA Cryptosystem Afterfindin
Page 38 and 39: 21 2.2 RSA Cryptosystem integer x <
Page 40 and 41: 23 2.3 Cryptanalysis of RSA to be h
Page 42 and 43: 25 2.3 Cryptanalysis of RSA The att
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 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 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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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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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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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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133 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
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