Introduction to cryptography with Maple:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2013
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XXX, 705 S. graph. Darst. |
| ISBN: | 3642321658 9783642321658 9783642446214 |
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MARC
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| 100 | 1 | |a Gómez Pardo, José Luis |d 1947- |e Verfasser |0 (DE-588)1041679157 |4 aut | |
| 245 | 1 | 0 | |a Introduction to cryptography with Maple |c José Luis Gómez Pardo |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2013 | |
| 300 | |a XXX, 705 S. |b graph. Darst. | ||
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Record in the Search Index
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IMAGE 1
CONTENTS
1 CLASSICAL CIPHERS AND THEIR CRYPTANALYSIS 1
1.1 THE CAESAR CIPHER 1
1.2 SUBSTITUTION CIPHERS 7
1.3 THE VIGENERE CIPHER 12
1.3.1 THE VIGENERE CIPHER IN MAPLE 14
1.3.2 CRYPTANALYSIS O F THE VIGENERE CIPHER 16
1.4 THE HILL CIPHER 25
1.4.1 THE HILL CIPHER IN MAPLE 27
1.4.2 CRYPTANALYSIS O F THE HILL CIPHER 29
1.5 SOME CONCLUSIONS 32
2 BASIC CONCEPTS FROM PROBABILITY, COMPLEXITY, ALGEBRA AND NUMBER THEORY
35
2.1 BASIC PROBABILITY THEORY 35
2.2 INTEGERS AND DIVISIBILITY 39
2.2.1 REPRESENTATION OF INTEGERS 4 0
2.3 BASIC COMPUTATIONAL COMPLEXITY 42
2.3.1 ASYMPTOTIC NOTATION 43
2.3.2 EFFICIENT COMPUTATION AND V VERSUS A F V 45
2.3.3 RUNNING TIMES O F SOME SIMPLE ALGORITHMS 51
2.3.4 PROBABILISTIC ALGORITHMS 58
2.3.5 FINAL REMARKS ON COMPLEXITY 6 0
2.4 THE EUCLIDEAN ALGORITHM 61
2.5 GROUPS, RINGS AND FIELDS 68
2.5.1 BASIC CONCEPTS 68
2.5.2 CONGRUENCES AND THE RESIDUE CLASS RING 73
2.6 THE CHINESE REMAINDER THEOREM 76
2.6.1 THE CHINESE REMAINDER THEOREM AND THE RESIDUE CLASS RING 78
XLLL
HTTP://D-NB.INFO/1024509591
IMAGE 2
X I V
C O N T E N T S
2.7 EULER'S THEOREM AND MODULAR EXPONENTIATION 80
2.7.1 EULER'S THEOREM 80
2.7.2 MODULAR EXPONENTIATION 83
2.7.3 FINDING GENERATORS IN Z* 89
2.8 FINITE FIELDS 95
2.8.1 A FIELD OF 4 ELEMENTS 95
2.8.2 THE POLYNOMIAL RING 99
2.8.3 THE FIELD OF P" ELEMENTS 104
2.8.4 THE FIELD OF 256 ELEMENTS I L L
2.8.5 THE MULTIPLICATIVE GROUP O F A FINITE FIELD 113
2.9 QUADRATIC RESIDUES AND MODULAR SQUARE ROOTS 115
2.9.1 QUADRATIC RESIDUES AND THE LEGENDRE AND JACOBI SYMBOLS 115
2.9.2 COMPUTING MODULAR SQUARE ROOTS 123
3 PRIVATE-KEY ENCRYPTION 131
3.1 PERFECT SECRECY 131
3.2 THE ONE-TIME PAD 135
3.3 FROM UNCONDITIONAL SECURITY TO COMPUTATIONAL SECURITY: PSEUDO-RANDOM
GENERATORS AND ONE-WAY FUNCTIONS 139
3.3.1 PSEUDO-RANDOM GENERATORS 139
3.3.2 ONE-WAY FUNCTIONS 144
3.3.3 FROM ONE-WAY FUNCTIONS TO PSEUDO-RANDOM GENERATORS: THE
BLUM-BLUM-SHUB PRG 148
3.4 PRGS AND RELATED CONSTRUCTIONS IN MAPLE 155
3.4.1 THE BLUM-BLUM-SHUB PRG IN MAPLE 156
3.4.2 AN APPROXIMATION TO THE ONE-TIME PAD IN MAPLE . . . 158
3.4.3 PRACTICAL SECURITY ASPECTS 162
3.5 PRIVATE-KEY ENCRYPTION SCHEMES AND THEIR SECURITY 167
3.5.1 PRIVATE-KEY ENCRYPTION SCHEMES 168
3.5.2 SECURITY DEFINITIONS FOR PRIVATE-KEY ENCRYPTION SCHEMES 169
3.5.3 CPA SECURITY AND CCA SECURITY 174
3.5.4 CONCLUDING REMARKS 178
4 BLOCK CIPHERS AND MODES O F OPERATION 181
4.1 BLOCK CIPHERS AND PSEUDO-RANDOM FUNCTIONS 181
4.2 THE ADVANCED ENCRYPTION STANDARD 186
4.2.1 THE DATA ENCRYPTION STANDARD 187
4.2.2 INTRODUCING AES 189
4.2.3 AES DECRYPTION 198
4.2.4 REMARKS ON AES DESIGN AND AES SECURITY 200
4.3 MODES OF OPERATION 202
4.3.1 CONFIDENTIALITY MODES 202
4.3.2 A CPA SECURE ENCRYPTION SCHEME 211
IMAGE 3
CONTENTS XV
4.4 AES IN MAPLE 216
4.4.1 AES OPERATIONS IN MAPLE 216
4.4.2 AES ENCRYPTION AND DECRYPTION 219
4.5 SOME MODES O F OPERATION IN MAPLE 222
4.5.1 OFB AND CTR IN MAPLE 222
4.5.2 ENCRYPTION AND DECRYPTION WITH OFB AND CTR 226
5 MESSAGE AUTHENTICATION 231
5.1 CONFIDENTIALITY VERSUS AUTHENTICITY 231
5.2 MESSAGE AUTHENTICATION CODES 233
5.2.1 DEFINING MACS 233
5.2.2 SECURITY FOR MACS 234
5.3 CONSTRUCTING MACS 236
5.3.1 MACS FROM PSEUDO-RANDOM FUNCTIONS 236
5.3.2 CBC-MAC 238
5.3.3 CMAC AND ITS MAPLE IMPLEMENTATION 240
5.4 CCA SECURITY AND AUTHENTICATED ENCRYPTION 244
5.4.1 A CCA SECURE ENCRYPTION SCHEME 244
5.4.2 OBTAINING AUTHENTICATED ENCRYPTION 246
5.5 MACS BASED ON UNIVERSAL HASHING 250
5.5.1 GCM 251
5.5.2 GMAC 256
5.6 COLLISION RESISTANT HASH FUNCTIONS 258
5.6.1 A COUPLE O F APPLICATIONS 260
5.6.2 THE MERKLE-DAMGARD CONSTRUCTION 261
5.6.3 SHA-256 263
5.6.4 SHA-256 IN MAPLE 264
5.6.5 MACS WITH HASH FUNCTIONS: HMAC 268
5.7 THE BIRTHDAY ATTACK ON HASH FUNCTIONS 271
5.7.1 THE BIRTHDAY PARADOX 271
5.7.2 THE BIRTHDAY ATTACK 274
6 ALGORITHMIC NUMBER THEORY FOR CRYPTOGRAPHY AND CRYPTANALYSIS:
PRIMALITY, FACTORING AND DISCRETE LOGARITHMS. . . . 283 6.1 LARGE PRIMES
AND HOW TO FIND THEM 283
6.1.1 SEARCHING FOR LARGE RANDOM PRIMES 284
6.1.2 THE DISTRIBUTION O F PRIME NUMBERS 286
6.2 PRIMALITY TESTING 292
6.2.1 THE FERMAT TEST AND PSEUDOPRIMES 292
6.2.2 THE STRONG PROBABLE PRIME TEST 299
6.2.3 THE MILLER-RABIN TEST 304
6.2.4 OTHER PRIMALITY TESTS 311
6.3 GENERATING RANDOM PRIMES 314
6.3.1 GENERATING SAFE PRIMES 317
6.3.2 GENERATING PSEUDO-RANDOM PRIMES WITH MAPLE 319
IMAGE 4
XVI CONTENTS
6.4 THE INTEGER FACTORIZATION PROBLEM 320
6.4.1 TRIAL DIVISION AS A FACTORING ALGORITHM 321
6.4.2 POLLARD'S RHO METHOD AND ITS MAPLE IMPLEMENTATION 323
6.4.3 FERMAT'S FACTORIZATION METHOD 326
6.4.4 FERMAT'S FACTORIZATION METHOD IN MAPLE 329
6.4.5 FACTOR BASES 334
6.4.6 THE FACTOR BASE METHOD IN MAPLE 340
6.4.7 THE QUADRATIC SIEVE 353
6.4.8 THE BASIC QS ALGORITHM IN MAPLE 358
6.4.9 SOME IMPROVEMENTS ON THE BASIC QS 364
6.4.10 THE CURRENT STATUS OF FACTORIZATION 366
6.5 THE DISCRETE LOGARITHM PROBLEM 371
6.5.1 THE BABY-STEP GIANT-STEP ALGORITHM AND ITS MAPLE IMPLEMENTATION
372
6.5.2 POLLARD'S RHO METHOD FOR DISCRETE LOGARITHMS 376
6.5.3 THE RHO METHOD FOR DISCRETE LOGARITHMS IN MAPLE 379
6.5.4 THE POHLIG-HELLMAN ALGORITHM AND ITS MAPLE IMPLEMENTATION 382
6.5.5 THE INDEX CALCULUS METHOD FOR DISCRETE LOGARITHMS 385
6.5.6 THE INDEX CALCULUS METHOD IN MAPLE 389
6.5.7 EXTENSIONS OF THE INDEX CALCULUS METHOD 395
6.5.8 FINAL REMARKS ON THE DISCRETE LOGARITHM PROBLEM. . . 397
7 INTRODUCTION TO PUBLIC-KEY CRYPTOGRAPHY: THE DIFFIE-HELLMAN PROTOCOL
399
7.1 FROM PRIVATE-KEY TO PUBLIC-KEY CRYPTOGRAPHY 399
7.2 THE DIFFIE-HELLMAN KEY AGREEMENT 403
7.2.1 THE DH PROTOCOL AND THE D H PROBLEMS 403
7.2.2 MAN-IN-THE-MIDDLE ATTACKS 407
7.2.3 GROUPS FOR THE DH PROTOCOL 408
7.2.4 ATTACKING THE DIFFIE-HELLMAN PROTOCOL WITH MAPLE 412
7.2.5 CONCLUDING REMARKS ON THE DIFFIE-HELLMAN PROTOCOL 416
8 PUBLIC-KEY ENCRYPTION 419
8.1 PUBLIC-KEY ENCRYPTION SCHEMES 419
8.2 SECURITY FOR PUBLIC-KEY ENCRYPTION 422
8.2.1 DEFINITIONS OF SECURITY 423
8.2.2 HYBRID ENCRYPTION AND ITS SECURITY 427
IMAGE 5
CONTENTS XVII
8.3 RSA 429
8.3.1 THE RSA ASSUMPTION 429
8.3.2 PLAIN RSA 434
8.3.3 PLAIN RSA IN MAPLE 440
8.3.4 SECURITY OF RSA 447
8.3.5 RSA WITH PROBABILISTIC ENCRYPTION 458
8.3.6 RSA-OAEP 461
8.3.7 RSAES-OAEP IN MAPLE 469
8.4 RABIN ENCRYPTION 475
8.4.1 PLAIN RABIN ENCRYPTION 475
8.4.2 PLAIN RABIN ENCRYPTION IN MAPLE 480
8.4.3 CCA SECURE RABIN ENCRYPTION 483
8.4.4 RABIN-SAEP+ IN MAPLE 489
8.5 THE ELGAMAL ENCRYPTION SCHEME 495
8.5.1 SECURITY O F ELGAMAL 497
8.5.2 ELGAMAL ON THE GROUP O F QUADRATIC RESIDUES MODULO A SAFE PRIME
501
8.6 THE CRAMER-SHOUP ENCRYPTION SCHEME 505
8.6.1 CRAMER-SHOUP ENCRYPTION AND ITS SECURITY 505
8.6.2 A VARIANT O F THE CRAMER-SHOUP ENCRYPTION SCHEME IN MAPLE 513
8.7 A SPEED COMPARISON AMONG IMPLEMENTATIONS O F CCA SECURE SCHEMES 520
8.8 HOMOMORPHIC ENCRYPTION 523
8.8.1 THE GOLDWASSER-MICALI ENCRYPTION SCHEME 523
8.8.2 THE PAILLIER ENCRYPTION SCHEME 526
8.8.3 THE PAILLIER ENCRYPTION SCHEME IN MAPLE 532
8.9 FINAL REMARKS ON PUBLIC-KEY ENCRYPTION 533
8.9.1 FULLY HOMOMORPHIC ENCRYPTION 534
8.9.2 LATTICE-BASED CRYPTOGRAPHY 535
9 DIGITAL SIGNATURES 537
9.1 DIGITAL SIGNATURE SCHEMES 538
9.1.1 DEFINITION OF SIGNATURE SCHEMES 538
9.1.2 SECURITY O F SIGNATURE SCHEMES 539
9.2 SOME EARLY SIGNATURE SCHEMES 541
9.2.1 PLAIN RSA SIGNATURES 541
9.2.2 ELGAMAL SIGNATURES 543
9.3 THE "HASH-THEN-DECRYPT" PARADIGM 544
9.3.1 HASHED RSA SIGNATURES 545
9.3.2 HASHED ELGAMAL SIGNATURES 546
9.4 THE DIGITAL SIGNATURE ALGORITHM 548
9.4.1 THE DSA SIGNATURE SCHEME 549
9.4.2 DSA SECURITY 551
9.4.3 DSA IN MAPLE 553
IMAGE 6
XV111
C O N T E N T S
9.5 CMA SECURE SIGNATURE SCHEMES 560
9.5.1 FDH SIGNATURES 560
9.5.2 PSS SIGNATURES 564
9.5.3 RSASSA-PSS FROM PKCS #1 V2.1 567
9.5.4 RSASSA-PSS IN MAPLE 570
9.5.5 CRAMER-SHOUP SIGNATURES 576
9.6 SIGNATURES WITH ADDED FUNCTIONALITY 578
9.6.1 BLIND SIGNATURES 578
9.6.2 OTHER SIGNATURES WITH ADDED FUNCTIONALITY 580
9.7 PUBLIC-KEY INFRASTRUCTURES 581
9.7.1 CERTIFICATES 581
9.7.2 MULTIPLE CERTIFICATION AUTHORITIES 583
10 IDENTITY-BASED CRYPTOGRAPHY 587
10.1 INTRODUCING IDENTITY-BASED CRYPTOGRAPHY 587
10.2 IDENTITY-BASED SIGNATURES 590
10.2.1 IBS SCHEMES 590
10.2.2 FROM SIGNATURE SCHEMES TO IBS SCHEMES 591
10.3 IDENTITY-BASED ENCRYPTION 593
10.3.1 IBE DEFINITION 593
10.3.2 APPLICATIONS O F IBE 594
10.3.3 THE COCKS IBE SCHEME 595
10.3.4 THE COCKS IBE SCHEME IN MAPLE 599
10.4 THE BONEH-FRANKLIN IBE SCHEME 605
10.4.1 PAIRINGS 605
10.4.2 THE BONEH-FRANKLIN SCHEME 607
10.5 FINAL REMARKS ON IDENTITY-BASED CRYPTOGRAPHY 610
11 AN INTRODUCTION TO ELLIPTIC CURVE CRYPTOGRAPHY 611
11.1 ELLIPTIC CURVES AND THEIR GROUP STRUCTURE 613
11.1.1 DEFINITION OF ELLIPTIC CURVE 613
11.1.2 THE GROUP STRUCTURE ON AN ELLIPTIC CURVE 616
11.2 ELLIPTIC CURVES OVER FINITE FIELDS 624
11.2.1 SOME SMALL EXAMPLES 624
11.2.2 ELLIPTIC CURVE ELEMENTARY COMPUTATIONS 626
11.2.3 THE ORDERS OF ELLIPTIC CURVE GROUPS 632
11.2.4 ELLIPTIC CURVE GROUPS OVER PRIME FIELDS IN MAPLE. . . 639 11.3
THE ELLIPTIC CURVE DISCRETE LOGARITHM PROBLEM 648
11.3.1 THE RHO METHOD AND POHLIG-HELLMAN FOR THE ECDLP IN MAPLE 649
11.3.2 THE CURRENT STATE O F THE ECDLP 653
11.3.3 REDUCTION ATTACKS AGAINST THE ECDLP 655
11.3.4 FINAL REMARKS ON THE ECDLP 660
IMAGE 7
CONTENTS XIX
11.4 ELLIPTIC CURVE SCHEMES 662
11.4.1 ECC SCHEMES AND THEIR DOMAIN PARAMETERS 662
11.4.2 THE ELLIPTIC CURVE DIGITAL SIGNATURE ALGORITHM (ECDSA) 665
11.4.3 ECDSA IN MAPLE 668
11.4.4 ELLIPTIC CURVE ENCRYPTION 673
11.5 FINAL REMARKS ON ELLIPTIC CURVE CRYPTOGRAPHY 676
APPENDIX A: SOME MAPLE CONVERSION FUNCTIONS 677
REFERENCES 685
INDEX 695 |
| any_adam_object | 1 |
| author | Gómez Pardo, José Luis 1947- |
| author_GND | (DE-588)1041679157 |
| author_facet | Gómez Pardo, José Luis 1947- |
| author_role | aut |
| author_sort | Gómez Pardo, José Luis 1947- |
| author_variant | p j l g pjl pjlg |
| building | Verbundindex |
| bvnumber | BV040742272 |
| classification_rvk | ST 276 ST 277 ST 601 |
| ctrlnum | (OCoLC)826902183 (DE-599)DNB1024509591 |
| dewey-full | 005.82 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 005 - Computer programming, programs, data, security |
| dewey-raw | 005.82 |
| dewey-search | 005.82 |
| dewey-sort | 15.82 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik |
| format | Book |
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| id | DE-604.BV040742272 |
| illustrated | Illustrated |
| indexdate | 2024-11-13T17:00:27Z |
| institution | BVB |
| isbn | 3642321658 9783642321658 9783642446214 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025722186 |
| oclc_num | 826902183 |
| open_access_boolean | |
| owner | DE-29T DE-11 |
| owner_facet | DE-29T DE-11 |
| physical | XXX, 705 S. graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| spelling | Gómez Pardo, José Luis 1947- Verfasser (DE-588)1041679157 aut Introduction to cryptography with Maple José Luis Gómez Pardo Berlin [u.a.] Springer 2013 XXX, 705 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Kryptoanalyse (DE-588)4830502-9 gnd rswk-swf Kryptologie (DE-588)4033329-2 gnd rswk-swf Maple Programm (DE-588)4209397-1 gnd rswk-swf Kryptologie (DE-588)4033329-2 s Maple Programm (DE-588)4209397-1 s DE-604 Kryptoanalyse (DE-588)4830502-9 s Erscheint auch als Online-Ausgabe 978-3-642-32166-5 application/pdf http://d-nb.info/1024509591/04 Inhaltsverzeichnis text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4091016&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025722186&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gómez Pardo, José Luis 1947- Introduction to cryptography with Maple Kryptoanalyse (DE-588)4830502-9 gnd Kryptologie (DE-588)4033329-2 gnd Maple Programm (DE-588)4209397-1 gnd |
| subject_GND | (DE-588)4830502-9 (DE-588)4033329-2 (DE-588)4209397-1 |
| title | Introduction to cryptography with Maple |
| title_auth | Introduction to cryptography with Maple |
| title_exact_search | Introduction to cryptography with Maple |
| title_full | Introduction to cryptography with Maple José Luis Gómez Pardo |
| title_fullStr | Introduction to cryptography with Maple José Luis Gómez Pardo |
| title_full_unstemmed | Introduction to cryptography with Maple José Luis Gómez Pardo |
| title_short | Introduction to cryptography with Maple |
| title_sort | introduction to cryptography with maple |
| topic | Kryptoanalyse (DE-588)4830502-9 gnd Kryptologie (DE-588)4033329-2 gnd Maple Programm (DE-588)4209397-1 gnd |
| topic_facet | Kryptoanalyse Kryptologie Maple Programm |
| url | http://d-nb.info/1024509591/04 http://deposit.dnb.de/cgi-bin/dokserv?id=4091016&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025722186&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT gomezpardojoseluis introductiontocryptographywithmaple |
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