Cryptanalysis of number theoretic ciphers:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2003
|
| Schriftenreihe: | Computational mathematics series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 318 S. |
| ISBN: | 1584881534 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | C O M P U T A T I O N A L M A T H E M A T I C S S E R I E S
CRYPTANALYSIS OF NUMBER THEORETIC CIPHERS SAMUEL S. WAGSTAFF, JR.
CHAPMAN & HALL/CRC A CRC PRESS COMPANY BOCA RATON LONDON NEW YORK
WASHINGTON, D.C. CONTENTS MATHEMATICAL FOUNDATIONS OF CRYPTANALYSIS 1
TERMINOLOGY OF CRYPTOGRAPHY 3 1.1 NOTATION 3 1.2 TYPES OF ATTACKS 4 1.3
PUBLIC KEY CIPHERS 6 1.4 BLOCK AND STREAM CIPHERS 7 1.5 PROTOCOLS 10 1.6
EXERCISES 10 PROBABILITY THEORY 13 2.1 DEFINITIONS 13 2.2 THE BIRTHDAY
PROBLEM 15 2.3 RANDOM VARIABLES 20 2.4 EXERCISES 24 DIVISIBILITY AND
ARITHMETIC 27 3.1 DIVISIBILITY 27 3.2 ARITHMETIC WITH LARGE INTEGERS 28
3.3 GREATEST COMMON DIVISORS AND THE EUCLIDEAN ALGORITHM ... 36 3.4
EXERCISES 42 PRIMES 45 4.1 THE FUNDAMENTAL THEOREM OF ARITHMETIC 45 4.2
THE DISTRIBUTION OF PRIME NUMBERS 49 4.3 IDENTIFYING AND FINDING PRIMES
51 4.4 THE LARGEST PRIME FACTOR OF A NUMBER 54 4.5 EXERCISES 59
CONGRUENCES 61 5.1 SIMPLE PROPERTIES OF CONGRUENCES 61 5.2 LINEAR
CONGRUENCES 64 5.3 THE CHINESE REMAINDER THEOREM 69 5.4 EXERCISES 72 XI
XII CONTENTS 6 EULER S THEOREM AND ITS CONSEQUENCES 75 6.1 FERMAT S
LITTLE THEOREM 75 6.2 EULER S THEOREM 79 6.3 PRIMITIVE ROOTS 86 6.4
DISCRETE LOGARITHMS 89 6.5 EXERCISES 91 7 SECOND DEGREE CONGRUENCES 93
7.1 THE LEGENDRE SYMBOL 94 7.2 THE LAW OF QUADRATIC RECIPROCITY 98 7.3
THE JACOBI SYMBOL 100 7.4 EULER PSEUDOPRIMES 103 7.5 SOLVING QUADRATIC
CONGRUENCES MODULO M 104 7.6 EXERCISES 110 8 INFORMATION THEORY 111 8.1
ENTROPY ILL 8.2 PERFECT SECRECY 114 8.3 UNICITY DISTANCE 115 8.4 SOME
OBSOLETE CIPHERS 117 8.5 THE ENTROPY OF NUMBER THEORETIC CIPHERS 121 8.6
EXERCISES 122 9 GROUPS, RINGS AND FIELDS 125 9.1 GROUPS 125 9.2 SIMPLE
PROPERTIES OF GROUPS 127 9.3 THE BABY-STEP-GIANT-STEP ALGORITHM 130 9.4
RINGS AND FIELDS 132 9.5 POLYNOMIALS 133 9.6 ALGEBRAIC NUMBER THEORY 137
9.7 EXERCISES 140 10 EXPONENTIAL METHODS OF FACTORING INTEGERS 143 10.1
FERMAT S DIFFERENCE OF SQUARES METHOD 143 10.2 POLLARD S RHO METHOD 146
10.3 POLLARD S P - 1 METHOD 149 10.4 SQUARE FORM FACTORIZATION 151 10.5
EXERCISES 153 11 FINDING LARGE PRIMES 155 11.1 STRONGER PROBABLE PRIME
TESTS 156 11.2 LUCAS PROBABLE PRIME TESTS 160 11.3 RIGOROUS PROOF OF
PRIMALITY 165 11.4 PRIME PROOFS FOR ARBITRARY LARGE INTEGERS 169 11.5
EXERCISES 169 CONTENTS XIII 12 ELLIPTIC CURVES 171 12.1 DEFINITIONS AND
EXAMPLES 171 12.2 FACTORING WITH ELLIPTIC CURVES 176 12.3 PRIMALITY
PROVING WITH ELLIPTIC CURVES 181 12.4 EXERCISES 182 13 SUBEXPONENTIAL
FACTORING ALGORITHMS 185 13.1 FACTORING WITH CONTINUED FRACTIONS 185
13.2 THE QUADRATIC SIEVE 190 13.3 VARIATIONS OF THE QUADRATIC SIEVE 193
13.3.1 LARGE PRIMES 193 13.3.2 MULTIPLE POLYNOMIALS 194 13.3.3 THE
SELF-INITIALIZING QUADRATIC SIEVE 195 13.4 THE NUMBER FIELD SIEVE 196
13.5 EXERCISES 201 14 COMPUTING DISCRETE LOGARITHMS 203 14.1 SHANKS
BABY-STEP-GIANT-STEP METHOD 204 14.2 POLLARD S METHODS 204 14.2.1 THE
RHO METHOD FOR DISCRETE LOGARITHMS 204 14.2.2 THE LAMBDA METHOD FOR
DISCRETE LOGARITHMS 205 14.3 DISCRETE LOGARITHMS VIA INDEX CALCULUS 206
14.4 OTHER FAST METHODS FOR THE GROUP R M 207 14.5 EXERCISES 210 15
RANDOM NUMBER GENERATION 211 15.1 LINEAR FEEDBACK SHIFT REGISTERS 212
15.2 A QUADRATIC RESIDUE RANDOM NUMBER GENERATOR 215 15.3 HASH FUNCTIONS
216 15.4 GENERATING TRULY RANDOM NUMBERS 217 15.5 EXERCISES 218 II THE
CRYPTOGRAPHIC ALGORITHMS 219 16 PRIVATE KEY CIPHERS 221 16.1 RIJNDAEL,
THE ADVANCED ENCRYPTION STANDARD 221 16.1.1 BYTE ARITHMETIC IN RIJNDAEL
222 16.1.2 WORD ARITHMETIC IN RIJNDAEL 224 16.1.3 THE STRUCTURE OF
RIJNDAEL 225 16.1.4 THE KEY SCHEDULE OF RIJNDAEL 227, 16.1.5 SUMMARY OF
RIJNDAEL 227 16.2 THE POHLIG-HELLMAN CIPHER 228 16.3 ELLIPTIC CURVE
POHLIG-HELLMAN 228 16.4 EXERCISES 230 XIV CONTENTS 17 PUBLIC KEY CIPHERS
231 17.1 RIVEST-SHAMIR-ADLEMAN 231 17.2 MASSEY-OMURA 232 17.3 ELLIPTIC
CURVE MASSEY-OMURA 233 17.4 ELGAMAL 233 17.5 ELLIPTIC CURVE ELGAMAL 234
17.6 RABIN-WILLIAMS 235 17.7 EXERCISES 237 18 SIGNATURE ALGORITHMS 239
18.1 RIVEST-SHAMIR-ADLEMAN SIGNATURES 239 18.2 ELGAMAL SIGNATURES 240
18.3 RABIN-WILLIAMS SIGNATURES 241 18.4 THE DIGITAL SIGNATURE ALGORITHM
242 18.5 EXERCISES 244 19 KEY EXCHANGE ALGORITHMS 245 19.1 KEY EXCHANGE
USING A TRUSTED SERVER 245 19.2 THE DIFFIE-HELLMAN KEY EXCHANGE 248 19.3
THE X.509 KEY EXCHANGE 249 19.4 EXERCISES 251 20 SIMPLE PROTOCOLS 253
20.1 BIT COMMITMENT 253 20.2 MENTAL POKER 253 20.3 OBLIVIOUS TRANSFER
255 20.4 ZERO-KNOWLEDGE PROOFS 256 20.5 METHODS OF SHARING SECRETS 258
20.5.1 SECRET SPLITTING 258 20.5.2 THE LAGRANGE INTERPOLATING POLYNOMIAL
SCHEME . . . . 258 20.5.3 THE ASMUTH AND BLOOM THRESHOLD SCHEME 260 20.6
BLIND SIGNATURES 261 20.7 EXERCISES 261 21 COMPLICATED PROTOCOLS 263
21.1 CONTRACT SIGNING 263 21.2 SECURE ELECTIONS 265 21.3 ELECTRONIC CASH
268 21.3.1 ELECTRONIC CASH ACCORDING TO CHAUM 268 21.3.2 ELECTRONIC CASH
ACCORDING TO BRANDS 271 21.4 EXERCISES 274 CONTENTS XV 22 COMPLETE
SYSTEMS 275 22.1 KERBEROS 275 22.2 PRETTY GOOD PRIVACY 277 22.3
EXERCISES 278 III METHODS OF ATTACK 279 23 DIRECT ATTACKS 281 23.1 TRY
ALL KEYS 281 23.2 FACTOR A LARGE INTEGER 283 23.3 SOLVE A DISCRETE
LOGARITHM PROBLEM 284 23.4 TIMING ATTACKS 286 23.5 EXERCISES 287 24
EXPLOITING AN ERROR 289 24.1 KEY MANAGEMENT 289 24.2 REUSE OF A KEY 290
24.3 BAD PARAMETER CHOICE 291 24.4 PARTIAL KEY EXPOSURE 293 24.5
COMPUTER FAILURE 293 24.6 EXERCISES 294 25 ACTIVE ATTACKS 297 25.1 FORCE
A USER TO MAKE A MISTAKE 297 25.2 MAN-IN-THE-MIDDLE ATTACKS 298 25.3
BIRTHDAY ATTACKS 300 25.4 SUBLIMINAL CHANNELS 300 25.5 EXERCISES 301
REFERENCES 303 INDEX 311
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| indexdate | 2024-07-09T19:05:51Z |
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| isbn | 1584881534 |
| language | English |
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| physical | XV, 318 S. |
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| spelling | Wagstaff, Samuel S. 1945- Verfasser (DE-588)117726672 aut Cryptanalysis of number theoretic ciphers Samuel S. Wagstaff, Jr Boca Raton [u.a.] Chapman & Hall/CRC 2003 XV, 318 S. txt rdacontent n rdamedia nc rdacarrier Computational mathematics series Computer security Cryptography Number theory Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Kryptologie (DE-588)4033329-2 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Kryptologie (DE-588)4033329-2 s Zahlentheorie (DE-588)4067277-3 s Algorithmus (DE-588)4001183-5 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009994134&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wagstaff, Samuel S. 1945- Cryptanalysis of number theoretic ciphers Computer security Cryptography Number theory Zahlentheorie (DE-588)4067277-3 gnd Kryptologie (DE-588)4033329-2 gnd Algorithmus (DE-588)4001183-5 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4033329-2 (DE-588)4001183-5 |
| title | Cryptanalysis of number theoretic ciphers |
| title_auth | Cryptanalysis of number theoretic ciphers |
| title_exact_search | Cryptanalysis of number theoretic ciphers |
| title_full | Cryptanalysis of number theoretic ciphers Samuel S. Wagstaff, Jr |
| title_fullStr | Cryptanalysis of number theoretic ciphers Samuel S. Wagstaff, Jr |
| title_full_unstemmed | Cryptanalysis of number theoretic ciphers Samuel S. Wagstaff, Jr |
| title_short | Cryptanalysis of number theoretic ciphers |
| title_sort | cryptanalysis of number theoretic ciphers |
| topic | Computer security Cryptography Number theory Zahlentheorie (DE-588)4067277-3 gnd Kryptologie (DE-588)4033329-2 gnd Algorithmus (DE-588)4001183-5 gnd |
| topic_facet | Computer security Cryptography Number theory Zahlentheorie Kryptologie Algorithmus |
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