Tài liệu Cryptography in C and C++

Foreword xiii
About the Author xv
About the Translator xvi
Preface to the Second American Edition xvii
Preface to the First American Edition xix
Preface to the First German Edition xxiii
I Arithmetic and Number Theory in C 1
1 Introduction 3
2 Number Formats: The Representation of Large Numbers in C 13
3 Interface Semantics 19
4 The Fundamental Operations 23
4.1 Addition and Subtraction 24
4.2 Multiplication 33
4.2.1 The Grade SchoolMethod . 34
4.2.2 Squaring Is Faster 40
4.2.3 Do Things Go Better with Karatsuba? . 45
4.3 Division with Remainder 50
5 Modular Arithmetic: Calculating with Residue Classes 67
6 Where All RoadsMeet:Modular Exponentiation 81
6.1 First Approaches 81
6.2 M-ary Exponentiation . 86
6.3 Addition Chains andWindows . 101
6.4 Montgomery Reduction and Exponentiation . 106
6.5 Cryptographic Application of Exponentiation . 118
7 Bitwise and Logical Functions 125
7.1 Shift Operations 125
7.2 All or Nothing: Bitwise Relations 131
7.3 Direct Access to Individual Binary Digits 137
7.4 Comparison Operators . 140
8 Input, Output, Assignment, Conversion 145
9 Dynamic Registers 157
10 Basic Number-Theoretic Functions 167
10.1 Greatest Common Divisor . 168
10.2 Multiplicative Inverse in Residue Class Rings . 175
10.3 Roots and Logarithms . 183
10.4 Square Roots in Residue Class Rings 191
10.4.1 The Jacobi Symbol . 192
10.4.2 Square RootsModulo pk 198
10.4.3 Square RootsModulo n . 203
10.4.4 Cryptography with Quadratic Residues 211
10.5 A Primality Test . 214
11 Rijndael: A Successor to the Data Encryption Standard 237
11.1 Arithmetic with Polynomials 239
11.2 The Rijndael Algorithm . 244
11.3 Calculating the Round Key . 247
11.4 The S-Box 248
11.5 The ShiftRowsTransformation . 249
11.6 The MixColumnsTransformation 250
11.7 The AddRoundKeyStep 252
11.8 Encryption as a Complete Process . 253
11.9 Decryption . 256
11.10 Performance 259
11.11 Modes of Operation 260
12 Large Random Numbers 261
12.1 A Simple Random Number Generator . 265
12.2 Cryptographic Random Number Generators . 268
12.2.1 The Generation of Start Values . 269
12.2.2 The BBS Random Number Generator . 273
12.2.3 The AES Generator . 279
12.2.4 The RMDSHA-1 Generator . 283
12.3 Quality Testing . 286
12.3.1 Chi-Squared Test 287
12.3.2 Monobit Test 289
12.3.3 Poker Test 289
12.3.4 Runs Test 289
12.3.5 Longruns Test 289
12.3.6 Autocorrelation Test 290
12.3.7 Quality of the FLINT/C Random Number Generators . 290
12.4 More Complex Functions 291
13 Strategies for Testing LINT 305
13.1 Static Analysis 307
13.2 Run-Time Tests . 309
II Arithmetic in C++ with the Class LINT 317
14 Let C++ Simplify Your Life 319
14.1 Not a Public Affair: The Representation of Numbers in LINT . 324
14.2 Constructors 325
14.3 Overloaded Operators . 329
15 The LINTPublic Interface:Members and Friends 337
15.1 Arithmetic . 337
15.2 Number Theory . 347
15.3 Stream I/O of LINTObjects . 352
15.3.1 Formatted Output of LINTObjects . 353
15.3.2 Manipulators 360
15.3.3 File I/O for LINTObjects . 362
16 Error Handling 367
16.1 (Don’t) Panic . 367
16.2 User-Defined Error Handling 369
16.3 LINTExceptions . 370
17 An Application Example: The RSA Cryptosystem 377
17.1 Asymmetric Cryptosystems 378
17.2 The RSA Algorithm . 380
17.3 Digital RSA Signatures . 395
17.4 RSA Classes in C++ . 403
18 Do It Yourself: Test LINT 413
19 Approaches for Further Extensions 417
III Appendices 419
A Directory of C Functions 421
A.1 Input/Output, Assignment, Conversions, Comparisons 421
A.2 Basic Calculations . 422
A.3 Modular Arithmetic . 423
A.4 Bitwise Operations . 425
A.5 Number-Theoretic Functions . 426
A.6 Generation of Pseudorandom Numbers 427
A.7 RegisterManagement . 431
B Directory of C++ Functions 433
B.1 Input/Output, Conversion, Comparison:Member Functions . 433
B.2 Input/Output, Conversion, Comparison: Friend Functions 436
B.3 Basic Operations:Member Functions . 438
B.4 Basic Operations: Friend Functions 439
B.5 Modular Arithmetic:Member Functions 440
B.6 Modular Arithmetic: Friend Functions . 442
B.7 Bitwise Operations:Member Functions 443
B.8 Bitwise Operations: Friend Functions . 444
B.9 Number-TheoreticMember Functions 445
B.10 Number-Theoretic Friend Functions . 446
B.11 Generation of Pseudorandom Numbers 450
B.12 Miscellaneous Functions 450
C Macros 451
C.1 Error Codes and Status Values . 451
C.2 Additional Constants 451
C.3 Macros with Parameters 453
D Calculation Times 459
E Notation 461
F Arithmetic and Number-Theoretic Packages 463
References 465
Index 473