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

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9 1.6 Prerequisites 1.6 Prerequisites Public Key Cryptography is a highly mathematical endeavor. RSA itself is based on the integer factorization problem, which has baffled the mathematicians for ages. TounderstandtheintricatedetailsofRSAandlattice-basedresultsproposed in this thesis, one requires a strong foundation in Mathematics. We frequently use involved results of number theory, linear algebra and probability in this thesis, and expect the reader to possess a good grasp on these topics. Although we present a comprehensive overview of all necessary mathematical preliminaries in Chapter 2, a graduate level training in mathematics is recommended to read the material comfortably.
Page 1: some results on Cryptanalysis of RS
Page 5 and 6: Abstract In this thesis, we propose
Page 7 and 8: Acknowledgements There are many peo
Page 9: 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: Chapter 1: Introduction 8 Chapter 5
Page 29 and 30: Chapter 2: Mathematical Preliminari
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
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59 3.3 A New Class of Weak Keys thi
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61 3.3 A New Class of Weak Keys to
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Chapter 4 Cryptanalysis of RSA with
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65 4.1 Theoretical Result Hence the
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67 4.1 Theoretical Result s,s 1 ,s
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69 4.1 Theoretical Result We want t
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71 4.1 Theoretical Result Calculati
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73 4.3 Conclusion share the integer
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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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