简介
Summary:
Publisher Summary 1
Practitioner Martin gives professionals who want to understand and implement identity-based encryption (IBE) much more than the fundamentals, providing practical techniques and algorithms, details on how and why certain IBE systems are secure, and numerous worked examples. He explains basic mathematical concepts and properties for novices, then advances as he describes the properties of elliptic curves in cryptography, divisors and the Tate pairing, cryptography and computational complexity, cryptographic algorithms, the Cocks and Boneh-Franklin IBE techniques, Boneh-Boyen and Sakai-Kasahara IBE schemes, hierarchical IBE, master secret sharing and the art of calculating pairings. Martin supplies summaries and references for each chapter and also an appendix with useful test data. Annotation 漏2008 Book News, Inc., Portland, OR (booknews.com)
目录
Preface p. xiii
Introduction p. 1
What Is IBE? p. 1
Why Should I Care About IBE? p. 8
References p. 13
Basic Mathematical Concepts and Properties p. 15
Concepts from Number Theory p. 15
Computing the GCD p. 16
Computing Jacobi Symbols p. 24
Concepts from Abstract Algebra p. 25
References p. 39
Properties of Elliptic Curves p. 41
Elliptic Curves p. 41
Adding Points on Elliptic Curves p. 47
Algorithm for Elliptic Curve Point Addition p. 52
Projective Coordinates p. 53
Adding Points in Jacobian Projective Coordinates p. 54
Doubling a Point in Jacobian Projective Coordinates p. 55
Algebraic Structure of Elliptic Curves p. 55
Higher Degree Twists p. 61
Complex Multiplication p. 65
References p. 66
Divisors and the Tate Pairing p. 67
Divisors p. 67
An Intuitive Introduction to Divisors p. 68
The Tate Pairing p. 76
Properties of the Tate Pairing p. 81
Miller's Algorithm p. 84
References p. 87
Cryptography and Computational Complexity p. 89
Cryptography p. 91
Definitions p. 91
Protection Provided by Encryption p. 93
The Fujisaki-Okamoto Transform p. 95
Running Times of Useful Algorithms p. 95
Finding Collisions for a Hash Function p. 96
Pollard's Rho Algorithm p. 98
The General Number Field Sieve p. 99
The Index Calculus Algorithm p. 102
Relative Strength of Algorithms p. 102
Useful Computational Problems p. 104
The Computational Diffie-Hellman Problem p. 105
The Decision Diffie-Hellman Problem p. 106
The Bilinear Diffie-Hellman Problem p. 107
The Decision Bilinear Diffie-Hellman Problem p. 107
q-Bilinear Diffie-Hellman Inversion p. 108
q-Decision Bilinear Diffie-Hellman Inversion p. 109
Cobilinear Diffie-Hellman Problems p. 109
Integer Factorization p. 109
Quadratic Residuosity p. 109
Selecting Parameter Sizes p. 110
Security Based on Integer Factorization and Quadratic Residuosity p. 110
Security Based on Discrete Logarithms p. 110
Important Special Cases p. 111
Anomalous Curves p. 112
Supersingular Elliptic Curves p. 112
Singular Elliptic Curves p. 113
Weak Primes p. 113
Proving Security of Public-Key Algorithms p. 114
Quantum Computing p. 116
Grover's Algorithm p. 116
Shor's Algorithm p. 117
References p. 118
Related Cryptographic Algorithms p. 121
Goldwasser-Michali Encryption p. 121
The Diffie-Hellman Key Exchange p. 124
Elliptic Curve Diffie-Hellman p. 125
Joux's Three-Way Key Exchange p. 126
ElGamal Encryption p. 128
References p. 129
The Cocks IBE Scheme p. 131
Setup of Parameters p. 131
Extraction of the Private Key p. 133
Encrypting with Cocks IBE p. 133
Decrypting with Cocks IBE p. 135
Examples p. 136
Security of the Cocks IBE Scheme p. 139
Relationship to the Quadratic Residuosity Problem p. 139
Chosen Ciphertext Security p. 142
Proof of Security p. 142
Selecting Parameter Sizes p. 143
Summary p. 143
References p. 145
Boneh-Franklin IBE p. 147
Boneh-Franklin IBE (Basic Scheme) p. 149
Setup of Parameters (Basic Scheme) p. 149
Extraction of the Private Key (Basic Scheme) p. 150
Encrypting with Boneh-Franklin IBE (Basic Scheme) p. 150
Decrypting with Boneh-Franklin IBE (Basic Scheme) p. 151
Examples (Basic Scheme) p. 151
Boneh-Franklin IBE (Full Scheme) p. 156
Setup of Parameters (Full Scheme) p. 156
Extraction of the Private Key (Full Scheme) p. 157
Encrypting with Boneh-Franklin IBE (Full Scheme) p. 157
Decrypting with Boneh-Franklin IBE (Full Scheme) p. 158
Security of the Boneh-Franklin IBE Scheme p. 158
Summary p. 159
Reference p. 160
Boneh-Boyen IBE p. 161
Boneh-Boyen IBE (Basic Scheme-Additive Notation) p. 162
Setup of Parameters (Basic Scheme-Additive Notation) p. 162
Extraction of the Private Key (Basic Scheme-Additive Notation) p. 164
Encrypting with Boneh-Boyen IBE (Basic Scheme-Additive Notation) p. 164
Decrypting with Boneh-Boyen IBE (Basic Scheme-Additive Notation) p. 164
Boneh-Boyen IBE (Basic Scheme-Multiplicative Notation) p. 168
Setup of Parameters (Basic Scheme-Multiplicative Notation) p. 168
Extraction of the Private Key (Basic Scheme-Multiplicative Notation) p. 170
Encrypting with Boneh-Boyen IBE (Basic Scheme-Multiplicative Notation) p. 170
Decrypting with Boneh-Boyen IBE (Basic Scheme-Multiplicative Notation) p. 170
Boneh-Boyen IBE (Full Scheme) p. 171
Setup of Parameters (Full Scheme) p. 172
Extraction of the Private Key (Full Scheme) p. 173
Encrypting with Boneh-Boyen IBE (Full Scheme) p. 173
Decrypting with Boneh-Boyen IBE (Full Scheme) p. 173
Security of the Boneh-Boyen IBE Scheme p. 174
Summary p. 175
Reference p. 176
Sakai-Kasahara IBE p. 177
Sakai-Kasahara IBE (Basic Scheme-Additive Notation) p. 177
Setup of Parameters (Basic Scheme-Additive Notation) p. 178
Extraction of the Private Key (Basic Scheme-Additive Notation) p. 178
Encrypting with Sakai-Kasahara IBE (Basic Scheme-Additive Notation) p. 180
Decrypting with Sakai-Kasahara IBE (Basic Scheme-Additive Notation) p. 180
Sakai-Kasahara IBE (Basic Scheme-Multiplicative Notation) p. 182
Setup of Parameters (Basic Scheme-Multiplicative Notation) p. 182
Extraction of the Private Key (Basic Scheme-Multiplicative Notation) p. 183
Encrypting with Sakai-Kasahara IBE (Basic Scheme-Multiplicative Notation) p. 184
Decrypting with Sakai-Kasahara IBE (Basic Scheme-Multiplicative Notation) p. 184
Sakai-Kasahara IBE (Full Scheme) p. 185
Setup of Parameters (Full Scheme) p. 185
Extraction of the Private Key (Full Scheme) p. 185
Encrypting with Sakai-Kasahara IBE (Full Scheme) p. 185
Decrypting with Sakai-Kasahara IBE (Full Scheme) p. 187
Security of the Sakai-Kasahara IBE Scheme p. 187
Summary p. 188
Reference p. 189
Hierarchial IBE and Master Secret Sharing p. 191
HIBE Based on Boneh-Franklin IBE p. 193
GS HIBE (Basic) Root Setup p. 194
GS HIBE (Basic) Lower-Level Setup p. 194
GS HIBE (Basic) Extract p. 194
GS HIBE (Basic) Encrypt p. 194
GS HIBE (Basic) Decrypt p. 195
Example of a GS HIBE System p. 195
GS HIBE (Basic) Root Setup p. 196
GS HIBE (Basic) Lower-Level Setup p. 196
GS HIBE (Basic) Extraction of Private Key p. 196
GS HIBE (Basic) Encryption p. 197
GS HIBE (Basic) Decryption p. 197
HIBE Based on Boneh-Boyen IBE p. 197
BBG HIBE (Basic) Setup p. 198
BBG HIBE (Basic) Extract p. 199
BBG HIBE (Basic) Encryption p. 199
BBG HIBE (Basic) Decryption p. 199
Example of a BBG HIBE System p. 200
BBG HIBE (Basic) Setup p. 200
BBG HIBE (Basic) Extraction of Private Key p. 200
BBG HIBE (Basic) Encryption p. 201
BBG HIBE (Basic) Decryption p. 201
Master Secret Sharing p. 201
Master Secret Sharing Example p. 202
References p. 204
Calculating Pairings p. 207
Pairing-Friendly Curves p. 207
Relative Efficiency of Parameters of Pairing-Friendly Curves p. 209
Eliminating Irrelevant Factors p. 210
Eliminating Random Components p. 211
Eliminating Extension Field Divisions p. 214
Denominator Elimination p. 215
Calculating the Product of Pairings p. 216
The Shipsey-Stange Algorithm p. 217
Precomputation p. 221
References p. 222
Useful Test Data p. 225
About the Author p. 229
Index p. 231
Introduction p. 1
What Is IBE? p. 1
Why Should I Care About IBE? p. 8
References p. 13
Basic Mathematical Concepts and Properties p. 15
Concepts from Number Theory p. 15
Computing the GCD p. 16
Computing Jacobi Symbols p. 24
Concepts from Abstract Algebra p. 25
References p. 39
Properties of Elliptic Curves p. 41
Elliptic Curves p. 41
Adding Points on Elliptic Curves p. 47
Algorithm for Elliptic Curve Point Addition p. 52
Projective Coordinates p. 53
Adding Points in Jacobian Projective Coordinates p. 54
Doubling a Point in Jacobian Projective Coordinates p. 55
Algebraic Structure of Elliptic Curves p. 55
Higher Degree Twists p. 61
Complex Multiplication p. 65
References p. 66
Divisors and the Tate Pairing p. 67
Divisors p. 67
An Intuitive Introduction to Divisors p. 68
The Tate Pairing p. 76
Properties of the Tate Pairing p. 81
Miller's Algorithm p. 84
References p. 87
Cryptography and Computational Complexity p. 89
Cryptography p. 91
Definitions p. 91
Protection Provided by Encryption p. 93
The Fujisaki-Okamoto Transform p. 95
Running Times of Useful Algorithms p. 95
Finding Collisions for a Hash Function p. 96
Pollard's Rho Algorithm p. 98
The General Number Field Sieve p. 99
The Index Calculus Algorithm p. 102
Relative Strength of Algorithms p. 102
Useful Computational Problems p. 104
The Computational Diffie-Hellman Problem p. 105
The Decision Diffie-Hellman Problem p. 106
The Bilinear Diffie-Hellman Problem p. 107
The Decision Bilinear Diffie-Hellman Problem p. 107
q-Bilinear Diffie-Hellman Inversion p. 108
q-Decision Bilinear Diffie-Hellman Inversion p. 109
Cobilinear Diffie-Hellman Problems p. 109
Integer Factorization p. 109
Quadratic Residuosity p. 109
Selecting Parameter Sizes p. 110
Security Based on Integer Factorization and Quadratic Residuosity p. 110
Security Based on Discrete Logarithms p. 110
Important Special Cases p. 111
Anomalous Curves p. 112
Supersingular Elliptic Curves p. 112
Singular Elliptic Curves p. 113
Weak Primes p. 113
Proving Security of Public-Key Algorithms p. 114
Quantum Computing p. 116
Grover's Algorithm p. 116
Shor's Algorithm p. 117
References p. 118
Related Cryptographic Algorithms p. 121
Goldwasser-Michali Encryption p. 121
The Diffie-Hellman Key Exchange p. 124
Elliptic Curve Diffie-Hellman p. 125
Joux's Three-Way Key Exchange p. 126
ElGamal Encryption p. 128
References p. 129
The Cocks IBE Scheme p. 131
Setup of Parameters p. 131
Extraction of the Private Key p. 133
Encrypting with Cocks IBE p. 133
Decrypting with Cocks IBE p. 135
Examples p. 136
Security of the Cocks IBE Scheme p. 139
Relationship to the Quadratic Residuosity Problem p. 139
Chosen Ciphertext Security p. 142
Proof of Security p. 142
Selecting Parameter Sizes p. 143
Summary p. 143
References p. 145
Boneh-Franklin IBE p. 147
Boneh-Franklin IBE (Basic Scheme) p. 149
Setup of Parameters (Basic Scheme) p. 149
Extraction of the Private Key (Basic Scheme) p. 150
Encrypting with Boneh-Franklin IBE (Basic Scheme) p. 150
Decrypting with Boneh-Franklin IBE (Basic Scheme) p. 151
Examples (Basic Scheme) p. 151
Boneh-Franklin IBE (Full Scheme) p. 156
Setup of Parameters (Full Scheme) p. 156
Extraction of the Private Key (Full Scheme) p. 157
Encrypting with Boneh-Franklin IBE (Full Scheme) p. 157
Decrypting with Boneh-Franklin IBE (Full Scheme) p. 158
Security of the Boneh-Franklin IBE Scheme p. 158
Summary p. 159
Reference p. 160
Boneh-Boyen IBE p. 161
Boneh-Boyen IBE (Basic Scheme-Additive Notation) p. 162
Setup of Parameters (Basic Scheme-Additive Notation) p. 162
Extraction of the Private Key (Basic Scheme-Additive Notation) p. 164
Encrypting with Boneh-Boyen IBE (Basic Scheme-Additive Notation) p. 164
Decrypting with Boneh-Boyen IBE (Basic Scheme-Additive Notation) p. 164
Boneh-Boyen IBE (Basic Scheme-Multiplicative Notation) p. 168
Setup of Parameters (Basic Scheme-Multiplicative Notation) p. 168
Extraction of the Private Key (Basic Scheme-Multiplicative Notation) p. 170
Encrypting with Boneh-Boyen IBE (Basic Scheme-Multiplicative Notation) p. 170
Decrypting with Boneh-Boyen IBE (Basic Scheme-Multiplicative Notation) p. 170
Boneh-Boyen IBE (Full Scheme) p. 171
Setup of Parameters (Full Scheme) p. 172
Extraction of the Private Key (Full Scheme) p. 173
Encrypting with Boneh-Boyen IBE (Full Scheme) p. 173
Decrypting with Boneh-Boyen IBE (Full Scheme) p. 173
Security of the Boneh-Boyen IBE Scheme p. 174
Summary p. 175
Reference p. 176
Sakai-Kasahara IBE p. 177
Sakai-Kasahara IBE (Basic Scheme-Additive Notation) p. 177
Setup of Parameters (Basic Scheme-Additive Notation) p. 178
Extraction of the Private Key (Basic Scheme-Additive Notation) p. 178
Encrypting with Sakai-Kasahara IBE (Basic Scheme-Additive Notation) p. 180
Decrypting with Sakai-Kasahara IBE (Basic Scheme-Additive Notation) p. 180
Sakai-Kasahara IBE (Basic Scheme-Multiplicative Notation) p. 182
Setup of Parameters (Basic Scheme-Multiplicative Notation) p. 182
Extraction of the Private Key (Basic Scheme-Multiplicative Notation) p. 183
Encrypting with Sakai-Kasahara IBE (Basic Scheme-Multiplicative Notation) p. 184
Decrypting with Sakai-Kasahara IBE (Basic Scheme-Multiplicative Notation) p. 184
Sakai-Kasahara IBE (Full Scheme) p. 185
Setup of Parameters (Full Scheme) p. 185
Extraction of the Private Key (Full Scheme) p. 185
Encrypting with Sakai-Kasahara IBE (Full Scheme) p. 185
Decrypting with Sakai-Kasahara IBE (Full Scheme) p. 187
Security of the Sakai-Kasahara IBE Scheme p. 187
Summary p. 188
Reference p. 189
Hierarchial IBE and Master Secret Sharing p. 191
HIBE Based on Boneh-Franklin IBE p. 193
GS HIBE (Basic) Root Setup p. 194
GS HIBE (Basic) Lower-Level Setup p. 194
GS HIBE (Basic) Extract p. 194
GS HIBE (Basic) Encrypt p. 194
GS HIBE (Basic) Decrypt p. 195
Example of a GS HIBE System p. 195
GS HIBE (Basic) Root Setup p. 196
GS HIBE (Basic) Lower-Level Setup p. 196
GS HIBE (Basic) Extraction of Private Key p. 196
GS HIBE (Basic) Encryption p. 197
GS HIBE (Basic) Decryption p. 197
HIBE Based on Boneh-Boyen IBE p. 197
BBG HIBE (Basic) Setup p. 198
BBG HIBE (Basic) Extract p. 199
BBG HIBE (Basic) Encryption p. 199
BBG HIBE (Basic) Decryption p. 199
Example of a BBG HIBE System p. 200
BBG HIBE (Basic) Setup p. 200
BBG HIBE (Basic) Extraction of Private Key p. 200
BBG HIBE (Basic) Encryption p. 201
BBG HIBE (Basic) Decryption p. 201
Master Secret Sharing p. 201
Master Secret Sharing Example p. 202
References p. 204
Calculating Pairings p. 207
Pairing-Friendly Curves p. 207
Relative Efficiency of Parameters of Pairing-Friendly Curves p. 209
Eliminating Irrelevant Factors p. 210
Eliminating Random Components p. 211
Eliminating Extension Field Divisions p. 214
Denominator Elimination p. 215
Calculating the Product of Pairings p. 216
The Shipsey-Stange Algorithm p. 217
Precomputation p. 221
References p. 222
Useful Test Data p. 225
About the Author p. 229
Index p. 231
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