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

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45 2.9 Conclusion 2.9 Conclusion Nowthatwehavecoveredthepreliminarytopicsofmathematicsandcryptography that constitute the foundation of this thesis, we can get into the technical results. In a major part of the thesis, the lattice based root finding techniques serve as a backbone. One may refer back to the preliminaries whenever similar methods in the following chapters are encountered.
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some results on Cryptanalysis of RS
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Abstract In this thesis, we propose
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Acknowledgements There are many peo
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To Thaakuma (Grandmother), the firs
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
Page 58 and 59: 41 2.6 Solving Integer Polynomials
Page 60 and 61: 43 2.7 Analysis of the Root Finding
Page 64 and 65: Chapter 3 A class of Weak Encryptio
Page 66 and 67: 49 3.1 Our Basic Technique Lemma 3.
Page 68 and 69: 51 3.1 Our Basic Technique • For
Page 70 and 71: 53 3.2 Improvements over Existing W
Page 72 and 73: 55 3.3 A New Class of Weak Keys 945
Page 74 and 75: 57 3.3 A New Class of Weak Keys 897
Page 76 and 77: 59 3.3 A New Class of Weak Keys thi
Page 78 and 79: 61 3.3 A New Class of Weak Keys to
Page 80 and 81: Chapter 4 Cryptanalysis of RSA with
Page 82 and 83: 65 4.1 Theoretical Result Hence the
Page 84 and 85: 67 4.1 Theoretical Result s,s 1 ,s
Page 86 and 87: 69 4.1 Theoretical Result We want t
Page 88 and 89: 71 4.1 Theoretical Result Calculati
Page 90: 73 4.3 Conclusion share the integer
Page 93 and 94: Chapter 5: Reconstruction of Primes
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Chapter 6: Implicit Factorization 9
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Chapter 7: Approximate Integer Comm
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Chapter 8 Conclusion In this chapte
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151 8.1 Summary of Technical Result
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153 8.2 Overview of Root Finding Te
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155 8.3 Open Problems Problem 8.3.
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Bibliography [1] Advanced Encryptio
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159 BIBLIOGRAPHY [20] Y.-G. Chen an
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161 BIBLIOGRAPHY [42] M. K. Frankli
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163 BIBLIOGRAPHY [65] E. Jochemsz a
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165 BIBLIOGRAPHY [86] A. May and M.
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167 BIBLIOGRAPHY [108] R. L. Rivest
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