Discrete algebraic methods: arithmetic, cryptography, automata and groups
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Berlin ; Boston
De Gruyter
[2016]
|
| Series: | De Gruyter textbook
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 342 Seiten Diagramme |
| ISBN: | 9783110413328 |
Staff View
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Record in the Search Index
| _version_ | 1804176267870732288 |
|---|---|
| adam_text | CONTENTS
P*E F OE C E _ V
1 ALGEBRAIC STRUCTURES * 1
1.1 GROUPS * ^
1.2 REGULAR POLYGONS 10* **
1.3 SYMMETRIC GROUPS * 13
1.4 RINGS * 15
1.5 MODULAR ARITHMETIC * 20
1.5.1 EUCLIDEAN ALGORITHM * 20
1.5.2 IDEALS IN THE INTEGERS * 22
1 .5 .3 SHINPQP R _ I N H P R T H P N R P M
* *
1.5.4 EULER*S TOTIENT FUNCTION _ 24
1.6 POLYNOMIALS AND FORMAL POWER SERIES * 26
1.7 HILBERT*S BASIS THEOREM * 32
1.8 FIELDS * 33
1.9 F *N ITE FIE LD S _ 3 5
1.10 UNITS MODULO 37* *
1.11 QUADRATIC RECIPROCITY * 38
EXERCISES * 41
SUMMARY * 46
2 CRYPTOGRAPHY
**
*
2.1 SYMMETRIC ENCRYPTION METHODS * 50
2.2 MONOALPHABETIC CIPHER * 52
2.3 POLYALPHABETIC CIPHER * 53
2.4 FREQUENCY ANALYSIS AND COINCIDENCE INDEX * 55
2.5 PERFECT SECURITY AND THE VERNAM ONE-TIME PAD * 56
2.6 ASYMMETRIC ENCRYPTION METHODS * 58
2.7 RSA CRYPTOSYSTEM* 60
2.8 RABIN CRYPTOSYSTEM * 61
2.9 DIFFIE-HELLMAN KEY EXCHANGE * 63
2.10 ELGAMAL CRYPTOSYSTEM * 64
2.11 CRYPTOGRAPHIC HASH FUNCTIONS * 65
2.12 DIGITAL SIGNATURES* 67
* * SECRET SHARING * 69
2.14 DIGITAL COMMITMENT 71
2.15 SHAMIR*S ATTACK ON THE MERKLE-HELLMAN CRYPTOSYSTEM * 73
EXERCISES * 78
SUMMARY * 81
3 NUMBER THEORETIC ALGORITHMS * 83
3.1 RUNTIME ANALYSIS OF ALGORITHMS * 83
3.2 FAST EXPONENTIATION _ 86
3.3 BINARY GCD * 87
3.4 PROBABILISTIC RECOGNITION OF PRIMES
*
88
3.4.1 FERMAT PRIMALLTY TEST AND CARMICHAEL NUMBERS * 88
3.4.2 SOLOVAY-STRASSEN PRLMALLTY TEST * 89
3.4.3 MILLER-RABIN PRIMALITY TEST90 ***
3.4.4 APPLICATIONS OF THE MILLER-RABIN SCHEME * 93
3.4.5 MILLER-IRABIN VERSUS SOLOVAY-STRASSEN * 95
3.5 EXTRACTING ROOTS IN FINITE FIELDS * 96
3.5.1 TONELLI*S ALGORITHM * 97
3.5.2 CLPOLLA.S ALGORITHM * 98
3.6 INTEGERFACTORIZATION * 99
3.6.1 POLLARD*S P 1 ** ALGORITHM * 100
3.6.2 POLLARD*S RHO ALGORITHM FOR FACTORIZATION * 100
3.6.3 QUADRATIC SIEVE * 101
3.7 DISCRETE LOGARITHM * 103
3.7.1 SHANKS, BABY-STEP GIANT-STEP ALGORITHM * 104
3.7.2 POLLARD*S RHO ALGORITHM FOR THE DISCRETE LOGARITHM * 105
3.7.3 POHLIG-HELLMAN ALGORITHM FOR GROUP ORDER REDUCTION * 106
3.7.4 INDEX CALCULUS * 107
3.8 MULTIPLICATION AND DIVISION * 108
3.9 DISCRETE FOURIER TRANSFORM * 109
3.10 PRIMITIVE ROOTS OF UNITY * 112
3.11 SCHOENHAGE_STRASSEN INTEGER MULTIPLICATION * 113
EXERCISES * 117
SUMMARY * 119
4 POLYNOMIAL * ME P*IMALITY TEST * 121
4.1 BASIC IDEA * 121
* 9 COMBINATORIAL TOOLS * 122
4.3 GROWTH OF THE LEAST COMMON MULTIPLE * 123
4.4 OF SMALL NUMBERS AND LARGE ORDERS * 125
4.5 AGRAWALKAYAL-SAXENA PRIMALITY TEST * 125
SUMMARY * 129
5 ELLIPTICCURVES * 131
5.1 GROUP LA W _ 1 3 5
5.1.1 LINES * 135
5.1.2 POLYNOMIALS OVER ELLIPTIC CU*V E S _ 1 3 7
5.1.3 DIVISO*S _ 1 4 1
5.1.4 PICARD GROUP143* *
5.2 APPLICATIONS OF ELLIPTIC CURVES * 144
5.2.1 DLFFIE-HELLMAN KEY EXCHANGE WITH ELLIPTIC CURVES* 145*
5.2.2 PSEUDOCURVES * 146
5.2.3 FACTORIZATION USING ELLIPTIC CURVES * 148
5.2.4 GOLDWASSER-KILIAN PRIMALITY CERTIFICATES * 150
5.3 ENDOMORPHISMS OF ELLIPTIC CURVES * 153
EXERCISES * 158
SUMMARY * 159
6 COMBINATORICS ON WORDS** 161
6.1 COMMUTATION
*
TRANSPOSITION AND CONJUGACY * 162
6.2 FINE AND W*LF*S PERIODICITY LEMMA * 164
6.3 KRUSKAL*S TREE THEOREM * 165
EXERCISES * 170
SUMMARY * 171
7 AUTOMATA** 173
7.1 RECOGNIZABLE SETS * 174
7.2 RATIONAL SETS * 181
7.3 REGULAR LANGUAGES** 186
7.4 STAR-FREE LANGUAGES * 189
7.5 KROHN-RHODES THEOREM * 193
7.6 GREEN.S RELATIONS * 205
7.7 AUTOMATA OVER INFINITE WORDS * 210
7.7.1 DETERMINISTIC BUCHI AUTOMATA * 211
7.7.2 UNION AND INTERSECTION
*
213
7.7.3 OMEGA-RATIONAL LANGUAGES * 214
7.7.4 RECOGNIZABILITY OF OMEGA-REGULAR LANGUAGES * 216
7.7.5 MONADIC SECOND-ORDER LOGE OVER INNMTE WORDS * 219
7.8 PRESBURGER ARITHMETIC * 223
7.9 SOLUTIONS OF LINEAR DIOPHANTINE SYSTEMS _ 228
EXERCISES * 231
SUMMARY * 234
8 DISCRETE INFINITE GROUPS * 236
S I CLASSICAL ALGORITHMIC PROBLEMS * 236
8.2 RESIDUALLY FINITE MONOIDS * 236
8.3 PRESENTATIONS * 237
8.4 REWRITING SYSTEMS * 238
8.4.1 TERMINATION AND CONFLUENCE * 238
8.4.2 SEMI*THUE SYSTEMS * 241
8.5 SOLVING THE WORD PROBLEM IN FINITELY PRESENTED MONOIDS * 246
8.6 FREE PARTIALLY COMMUTATIVE MONOIDS AND GROUPS _ 248
8.7 SEMLDIRECT PRODUCTS * 252
8.8 AMALGAMATED PRODUCTS AND HNN EXTENSIONS * 253
8.9 RATIONAL SETS AND BENOIS. THEOREM * 259
8.10 FREE GROUPS * 262
8.11 THE AUTOMORPHISM GROUP OF FREE GROUPS* 268 *
8.12 THE SPECIAL LINEAR GROUP SL(2*
* )
* 277
EXERCISES** 281
SUMMARY * 284
SOLUTIONS TO EXERCISES * 286
CHAPTERL * 286
CHAPTER 2 * 293
CHAPTER3 * 297
CHAPTER * 303
CHAPTER 6 * 306
CHAPTER 7 * 308
CHAPTERS * 318
BIBLIOGRAPHY * 325
INDEX * 329
|
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| spelling | Discrete algebraic methods arithmetic, cryptography, automata and groups Volker Diekert, Manfred Kufleitner, Gerhard Rosenberger, Ulrich Hertrampf Berlin ; Boston De Gruyter [2016] © 2016 XII, 342 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier De Gruyter textbook Algebraische Methode (DE-588)4141841-4 gnd rswk-swf Diskrete Mathematik (DE-588)4129143-8 gnd rswk-swf Fachhochschul-/Hochschulausbildung (DE-588)4123623-3 Lehrbuch gnd-content Diskrete Mathematik (DE-588)4129143-8 s Algebraische Methode (DE-588)4141841-4 s DE-604 Diekert, Volker 1955- Sonstige (DE-588)129845353 oth Kufleitner, Manfred Sonstige (DE-588)132169347 oth Rosenberger, Gerhard 1944- Sonstige (DE-588)13155221X oth Hertrampf, Ulrich 1956- Sonstige (DE-588)174103646 oth Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, EPUB 978-3-11-041632-9 Erscheint auch als Online-Ausgabe, PDF 978-3-11-041333-5 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028998252&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Discrete algebraic methods arithmetic, cryptography, automata and groups Algebraische Methode (DE-588)4141841-4 gnd Diskrete Mathematik (DE-588)4129143-8 gnd |
| subject_GND | (DE-588)4141841-4 (DE-588)4129143-8 (DE-588)4123623-3 |
| title | Discrete algebraic methods arithmetic, cryptography, automata and groups |
| title_auth | Discrete algebraic methods arithmetic, cryptography, automata and groups |
| title_exact_search | Discrete algebraic methods arithmetic, cryptography, automata and groups |
| title_full | Discrete algebraic methods arithmetic, cryptography, automata and groups Volker Diekert, Manfred Kufleitner, Gerhard Rosenberger, Ulrich Hertrampf |
| title_fullStr | Discrete algebraic methods arithmetic, cryptography, automata and groups Volker Diekert, Manfred Kufleitner, Gerhard Rosenberger, Ulrich Hertrampf |
| title_full_unstemmed | Discrete algebraic methods arithmetic, cryptography, automata and groups Volker Diekert, Manfred Kufleitner, Gerhard Rosenberger, Ulrich Hertrampf |
| title_short | Discrete algebraic methods |
| title_sort | discrete algebraic methods arithmetic cryptography automata and groups |
| title_sub | arithmetic, cryptography, automata and groups |
| topic | Algebraische Methode (DE-588)4141841-4 gnd Diskrete Mathematik (DE-588)4129143-8 gnd |
| topic_facet | Algebraische Methode Diskrete Mathematik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028998252&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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