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

More documents

Recommendations

Info

Chapter 1 Introduction The word ‘Cryptology’ originates from the Greek root words ‘kryptós’ (hidden) and ‘logia’ (study). So, quite literally, cryptology is the study and practice of hiding information, that is, the art and science of information security. It is quite natural that the notion of security requires the presence of an adversary, and any system must be tested against all potential attacks. Based on this idea, cryptology has been branched into two parts - Cryptography and Cryptanalysis. While cryptography ensures secure communication between two parties over insecure communication channels (telephone, courier, fax, e-mail etc.), the field of cryptanalysis deals with the study of breaking a cryptographic scheme by obtaining the classified information without authorization. Cryptology was used vastly in ancient civilizations throughout the world. Around 3000 BC, the Egyptians could communicate securely by writing messages in the coded Hieroglyph. ‘Artha-Sastra’ by the renowned Indian politician Kautilya (350–283 BC) discussed the use of cryptology in political circles. Julius Caesar (100–44 BC) used the Caesar cipher to send confidential messages. The subject resurrected and evolved in a completely new form at the dawn of the modern information era. During World War II, cryptology gained much more importance in political affairs. It was the famous episode of Enigma that made the worldawareofthepotentialpowerofthesubject. Today, cryptologyhasearnedits repute as a prime branch of modern science that deals with information security issues in the arena of digital globalization. It is used for numerous purposes of everyday life, including Internet banking, identification cards, secure databases, e-mails, social networking, and many more. 1
Chapter 1: Introduction 2 The motive of Cryptography, as it stands in the modern society, has broadened to cover not only encryption and decryption, but all of the following categories. Confidentiality deals with the process of encryption and decryption of data. This is the basic goal of cryptography that ensures secure data communication over insecure channels, possibly at the presence of a malicious adversary. DataIntegrity isthemechanismtocheckandmakesurethatthedatahasnotbeen tampered. This process is important to verify the consistency of the data and make sure no alterations have been made to the original communication. Authentication ensures proper identification of the sender (entity authentication), and the identification of the origin of communicated data (data origin authentication). This feature is required to ensure that data is accepted only from the authorized senders. Non-Repudiation is another important aspect of cryptography to solve disputes between the sender and the receiver. It may happen that the sender, after communicating some data, maliciously claims that he/she has not sent it at all. Non-repudiation provides the receiver with a proof to refute this claim. The proof can also be presented to a third-party arbitrator in such a case. In this thesis, we mainly concentrate on the Confidentiality aspect of cryptosystems. For further details about modern day Cryptology, one may refer to “Cryptography - Theory and Practice” by D. R. Stinson [126], or “Handbook of Applied Cryptography” by A. J. Menezes, P. C. van Oorschot and S. A. Vanstone [87]. An interested reader may also refer to “The Code Book” by S. Singh [122] to know the exciting history of evolution of the subject. 1.1 Encryption and Decryption Let us turn our attention to the functional aspect of a cryptographic scheme for confidentiality. In this section, we shall introduce the notions of encryption, decryption and the respective keys associated with these operations. Suppose Alice wants to send some plaintext M to Bob, and Charles is a malicious adversary who is eavesdropping on the insecure channel of communication. The scenario is as shown in Figure 1.1. Using some encryption function E, Alice
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: List of Figures 1.1 Communication o
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 62: 45 2.9 Conclusion 2.9 Conclusion No
Page 65 and 66: Chapter 3: A class of Weak Encrypti
Page 67 and 68: Chapter 3: A class of Weak Encrypti
Page 69 and 70:
Chapter 3: A class of Weak Encrypti
Page 71 and 72:
Page 73 and 74:
Page 75 and 76:
Page 77 and 78:
Page 79 and 80:
Page 81 and 82:
Chapter 4: Cryptanalysis of RSA wit
Page 83 and 84:
Page 85 and 86:
Page 87 and 88:
Page 89 and 90:
Page 92 and 93:
Chapter 5 Reconstruction of Primes
Page 94 and 95:
77 5.1 LSB Case: Combinatorial Anal
Page 96 and 97:
Page 98 and 99:
Page 100 and 101:
Page 102 and 103:
85 5.2 LSB Case: Lattice Based Tech
Page 104 and 105:
87 5.3 MSB Case: Our Method and its
Page 106 and 107:
Page 108 and 109:
Page 110 and 111:
Page 112 and 113:
Chapter 6 Implicit Factorization In
Page 114 and 115:
97 6.1 Implicit Factoring of Two La
Page 116 and 117:
99 6.1 Implicit Factoring of Two La
Page 118 and 119:
101 6.1 Implicit Factoring of Two L
Page 120 and 121:
Page 122 and 123:
Page 124 and 125:
107 6.2 Two Primes with Shared Cont
Page 126 and 127:
109 6.2 Two Primes with Shared Cont
Page 128 and 129:
111 6.3 Exposing a Few MSBs of One
Page 130 and 131:
113 6.3 Exposing a Few MSBs of One
Page 132 and 133:
Chapter 7 Approximate Integer Commo
Page 134 and 135:
117 7.1 Finding q −1 mod p ≡ Fa
Page 136 and 137:
119 7.2 Finding Smooth Integers in
Page 138 and 139:
121 7.3 Extension of Approximate Co
Page 140 and 141:
123 7.4 The General Solution for EP
Page 142 and 143:
Page 144 and 145:
Page 146 and 147:
Page 148 and 149:
Page 150 and 151:
133 7.5 Sublattice and Generalized
Page 152 and 153:
Page 154 and 155:
Page 156 and 157:
139 7.6 Improved Results for Larger
Page 158 and 159:
141 7.6 Improved Results for Larger
Page 160 and 161:
143 7.7 EGACDP The approach in this
Page 162 and 163:
145 7.7 EGACDP Sinceinthiscasethema
Page 164:
147 7.8 Conclusion poly{loga,k}. Th
Page 167 and 168:
Chapter 8: Conclusion 150 Chapter 3
Page 169 and 170:
Chapter 8: Conclusion 152 p 1 ,p 2
Page 171 and 172:
Chapter 8: Conclusion 154 represent
Page 173 and 174:
Chapter 8: Conclusion 156 Final Wor
Page 175 and 176:
BIBLIOGRAPHY 158 [9] J. Blömer and
Page 177 and 178:
BIBLIOGRAPHY 160 [31] B. de Weger.
Page 179 and 180:
BIBLIOGRAPHY 162 [54] M.J.Hinek. Cr
Page 181 and 182:
BIBLIOGRAPHY 164 [76] A. K. Lenstra
Page 183 and 184:
BIBLIOGRAPHY 166 [97] A. Nitaj. Cry
Page 185:
BIBLIOGRAPHY 168 [121] C. L. Siegel
show all

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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?