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

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some results on Cryptanalysis of RSA and Factorization A thesis presented to the Indian Statistical Institute in fulfillment of the thesis requirement for the degree of Doctor of Philosophy in Mathematics by Santanu Sarkar under the supervision of Professor Subhamoy Maitra Applied Statistics Unit INDIAN STATISTICAL INSTITUTE Kolkata, West Bengal, India, 2011
Page 1: some results on Cryptanalysis of RS
Page 6 and 7: In PKC 2009, May and Ritzenhofen pr
Page 8 and 9: and support they provided throughou
Page 11 and 12: Contents 1 Introduction 1 1.1 Encry
Page 13 and 14: 5 Reconstruction of Primes given fe
Page 15: List of Tables 3.1 The numerical up
Page 18 and 19: Chapter 1 Introduction The word ‘
Page 20 and 21: 3 1.2 Symmetric Key Cryptography en
Page 22 and 23: 5 1.3 Asymmetric Key Cryptography t
Page 24 and 25: 7 1.5 Organization of the Thesis 1.
Page 26: 9 1.6 Prerequisites 1.6 Prerequisit
Page 29 and 30: Chapter 2: Mathematical Preliminari
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Chapter 2: Mathematical Preliminari
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Chapter 3 A class of Weak Encryptio
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49 3.1 Our Basic Technique Lemma 3.
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51 3.1 Our Basic Technique • For
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53 3.2 Improvements over Existing W
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55 3.3 A New Class of Weak Keys 945
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57 3.3 A New Class of Weak Keys 897
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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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