Cryptanalytic Attacks on Rsa

by Yan, Song Y.

ISBN13: 9780387487410

ISBN10: 0387487417

Format: Hardcover

Pub. Date: 2007-11-16

Publisher(s): Springer Verlag

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Summary

RSA is the first workable and practicable public-key cryptographic system, based on the use of large prime numbers. It is also the most popular and widely-used cryptographic system in today's digital world, for which its three inventors Rivest, Shamir and Adleman received the year 2002 Turing Award, the equivalent Nobel Prize in Computer Science.Cryptanalytic Attacks on RSA covers almost all major known cryptanalytic attacks and defenses of the RSA cryptographic system and its variants. Since RSA depends heavily on computational complexity theory and number theory, background information on complexity theory and number theory is presented first. This is followed by an account of the RSA cryptographic system and its variants.Cryptanalytic Attacks on RSA is designed for a professional audience of practitioners and researchers in industry and academia and as a reference or secondary text for advanced level students in computer science, applied mathematics, electrical & communication engineering.

Author Biography

Song Y. Yan is Professor of Computer Science and Mathematics and Director of the Institute for Research in Applicable Computing at the University of Bedfordshire, England.

Preface	p. xi
Notations	p. xv
Computational/Mathematical Preliminaries	p. 1
Introduction	p. 1
Computability, Complexity and Intractability	p. 4
Efficient Number-Theoretic Algorithms	p. 15
Intractable Number-Theoretic Problems	p. 41
Chapter Notes and Further Reading	p. 54
RSA Public-Key Cryptography	p. 55
Introduction	p. 55
Public-Key Cryptography	p. 60
RSA Public-Key Cryptography	p. 66
RSA Problem and RSA Assumption	p. 71
RSA-Type Crytposystems	p. 73
Chapter Notes and Further Readings	p. 88
Integer Factorization Attacks	p. 91
Introduction	p. 91
Fermat Factoring Attack	p. 93
The "p ± 1" and ECM Attacks	p. 94
Quadratic Sieve Attack	p. 98
Successful QS Attack	p. 103
Number Field Sieve Attack	p. 105
Chapter Notes and Further Reading	p. 110
Discrete Logarithm Attacks	p. 111
Introduction	p. 111
Baby-Step Giant-Step Attack	p. 115
Silver-Pohlig-Hellman Attack	p. 118
Index Calculus Attacks	p. 122
Xedni Calculus Attack	p. 127
Chapter Notes and Further Reading	p. 132
Quantum Computing Attacks	p. 135
Introduction	p. 135
Order Finding Problem	p. 137
Quantum Order Finding Attack	p. 139
Quantum Integer Factorization Attack	p. 142
Quantum Discrete Logarithm Attack	p. 146
Chapter Notes and Further Reading	p. 148
Simple Elementary Attacks	p. 149
Introduction	p. 149
Guessing Plaintext Attacks	p. 150
Blinding Attack on RSA Signatures	p. 151
Guessing ¿(N) Attack	p. 152
Guessing d Attack	p. 155
eth Root Attack	p. 159
Common Modulus Attack	p. 161
Fixed-Point Attack	p. 164
Chapter Notes and Further Readings	p. 166
Public Exponent Attacks	p. 169
Introduction	p. 169
A Theorem of Coppersmith	p. 170
Short e Attacks for Same Messages	p. 173
Short e Attacks for Related Messages	p. 177
Lattice Attack for Stereotyped Messages	p. 183
Chapter Notes and Further Reading	p. 187
Private Exponent Attacks	p. 189
Introduction	p. 189
Diophantine Attack	p. 190
Extended Diophantine Attacks	p. 195
Small Private CRT-Exponent Attacks	p. 198
Partial Private Key Exposure Attacks	p. 201
Chapter Notes and Further Reading	p. 205
Side-Channel Attacks	p. 207
Introduction	p. 207
Modular Exponentiation Revisited	p. 208
Timing Attacks	p. 209
Time Attacks on RSA in OpenSSL	p. 212
Power (Analysis) Attacks	p. 215
Random Fault Attacks	p. 216
Chapter Notes and Further Reading	p. 222
The Road Ahead	p. 223
Introduction	p. 223
Elliptic Curve-Based Cryptography	p. 224
Coding-Based Cryptography	p. 225
Lattice-Based Cryptography	p. 227
Quantum Cryptography	p. 229
Conclusions	p. 230
Chapter Notes and Further Reading	p. 232
Bibliography	p. 233
Index	p. 251
About the Author	p. 255
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