Computer verification of algorithms using a formal proof system:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
dissertation.de
2010
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| Ausgabe: | Als Ms. gedr. |
| Schriftenreihe: | dissertation.de
1583 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 198 S. graph. Darst. 25 cm |
| ISBN: | 9783866244832 |
Internformat
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Datensatz im Suchindex
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| adam_text | CONTENTS LIST OF FIGURES 17 1 INTRODUCTION 19 2 CONTEXT 29 2.1
MATHEMATICAL LOGIC AND PROOF AUTOMATION 29 2.1.1 MOTIVATING EXAMPLES 29
2.1.2 LOGICAL VERIFICATION 31 2.1.3 AUTOMATED AND INTERACTIVE
VERIFICATION 32 2.2 HISTORY OF COMPUTER PROVING IN PREDICATE LOGIC 33
2.2.1 BOYER-MOORE FAMILY 33 2.2.2 HIGHER-ORDER LOGIC 34 2.3 THE MODEL 38
2.3.1 AIM OF COMPUTER PROVING 38 2.3.2 FORMAL VERIFICATION OF ALGORITHMS
39 2.3.3 A CRYPTOGRAPHIC CLIENT APPLICATION 40 2.3.4 CLIENT
IMPLEMENTATION/VERIFICATION 40 2.3.5 A DOMAIN OF EXPERTS 41 2.3.6
PROBLEM HANDLING 41 2.3.7 A KIND OF PROOF PATTERN 41 3 BACKGROUND 43 3.1
MATHEMATICAL BACKGROUND 43 3.1.1 INTRODUCTION TO CRYPTOGRAPHY 43 3.1.2
ASPECTS OF NUMBER THEORY 48 3.1.3 LOGIC AND CALCULI 51 3.2 OVERVIEW ON
TRAVERSAL ALGORITHMS 63 3.2.1 REWRITE RULES 64 3.2.2 ELEMENTARY
STRATEGIES/ BASIC COMBINATORE 64 3.2.3 AUXILIARY STRATEGIES 66 3.2.4
TRAVERSAL COMBINATORE 66 3.2.5 HIGHER-ORDER TRAVERSAL ALGORITHMS 67
3.2.6 A MOTIVATING EXAMPLE 67 3.3 FORMAL FRAMEWORK AND VERIFICATION IN
HOL 68 3.3.1 FORMAL FRAMEWORK 68 3.3.2 HOL AND FUNCTIONS 69 3.3.3
THEORIES 70 13 BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1004229194
DIGITALISIERT DURCH 14 CONTENTS 4 PRIMALITY IN PUBLIC-KEY CRYPTOGRAPHY
73 4.1 FORMAL PROBABILITY THEORY AND BAYES FORMULA 73 4.1.1 CLASSICAL
PROBABILITY THEORY 74 4.1.2 AXIOMATIC PROBABILITY THEORY 75 4.1.3
FUNDAMENTAL LEMMATA AND BAYES FORMULA 76 4.1.4 CRYPTOGRAPHIC
APPLICATION OF THE FORMAL FRAMEWORK . . . 77 4.1.5 APPLICATION OF FORMAL
PROBABILITY THEORY 79 4.1.6 A COMPLEXITY METRICS OF THE FORMAL MODEL 80
4.1.7 BIBLIOGRAPHIC CONCLUSION 80 4.2 FORMALIZED ASPECTS OF CRYPTOGRAPHY
80 4.2.1 OAEP 81 4.2.2 HASH FUNCTIONS 82 4.2.3 COMPLEXITY METRICS OF THE
FORMAL ASPECTS 86 4.3 MILLER-RABIN ALGORITHM 86 4.3.1 PRIMALITY OR
COMPOSITENESS 87 4.3.2 MILLER-RABIN ALGORITHM - OVERVIEW 89 4.3.3
MILLER-RABIN ALGORITHM - IMPLEMENTATION 89 4.3.4 MILLER-RABIN ALGORITHM
- CORRECTNESS 91 4.4 VERIFICATION OF MILLER-RABIN ALGORITHM 92 4.4.1
FORMALIZED MATHEMATICAL PROPERTIES 92 4.4.2 IMPLEMENTATION OF ALGORITHM
PRIM 93 4.4.3 IMPLEMENTATION OF ALGORITHM OPTIMIZEDPRIM 94 4.4.4
VERIFICATION OF ALGORITHM PRIM 96 4.4.5 VERIFICATION OF ALGORITHM
OPTIMIZEDPRIM 97 4.5 MILLER-RABIN ALGORITHM - CONCLUSION 99 5
VERIFICATION IN PUBLIC-KEY CRYPTOGRAPHY 101 5.1 RABIN PUBLIC-KEY SCHEME
101 5.1. CONTENTS 15 6 A FORMAL MODEL FOR TRAVERSAL ALGORITHMS 127 6.1
MOTIVATION 128 6.1.1 CONSTANT PROPAGATION 128 6.1.2 PARALLEL RENAMING
129 6.1.3 DEFINITION UNFOLDING 129 6.2 BACKGROUND 130 6.2.1
PRIMITIVES/COMBINATORS 130 6.2.2 A LIBRARY 132 6.3 BASIC FORMAL MODEL
132 6.3.1 THE TERMS THEORY 133 6.3.2 THE PRIMITIVES THEORY 133 6.4
RELATION TO OPERATIONAL RULES 136 6.4.1 BASIC TRANSLITERATION 136 6.4.2
INDEXED-BOUND TRANSLITERATION 136 6.5 ALGEBRAIC LAWS 137 6.5.1 LAWS FOR
SEQUENCE AND CHOICE 138 6.5.2 LAWS FOR ALL AND ONE 138 6.5.3 FUSION LAW
FOR ALL 139 7 VERIFICATION OF HIGHER-ORDER TRAVERSAL ALGORITHMS 141 7.1
MODELING PARTIAL STRATEGIES 141 7.1.1 FORMALIZING TRY 141 7.1.2 A
PROBLEM IN FORMALIZING REPEAT 142 7.1.3 OVERVIEW OF THE APPROACH 142
7.1.4 IDENTIFICATION OF TERMINATION CONDITIONS 143 7.1.5 A RELATIONAL
DEFINITION OF REPEAT 143 7.1.6 THE FUNCTIONAL PROPERTY OF A RELATION 143
7.1. 8 MODELING AND PROVING IN HOL * A DISCUSSION 161 8.1 FORMAL
VERIFICATION IN GENERAL 161 8.1.1 GENERAL OVERVIEW 161 8.1.2
VERIFICATION APPROACH 162 8.1.3 A KIND OF INTERFACE 163 8.1.4 MODELING
PARTIAL FUNCTIONS 163 8.1.5 IMPROVED PROVING 166 8.1.6 PROOF EXPERIENCE
166 8.2 ELLIPTIC CURVE CRYPTOGRAPHY 167 8.3 ALGEBRAIC TRAVERSAL
ALGORITHMS AND FUNCTIONS 168 9 CONCLUSION 171 9.1 REVIEW 171 9.2
LIMITATIONS 174 9.3 WORK FOR THE FUTURE 175 9.3.1 VERIFYING CRYPTOGRAPHY
175 9.3.2 TRAVERSAL ALGORITHMS AND FUNCTIONS 175 APPENDIX 179
BIBLIOGRAPHY 183 INDEX 195
|
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| discipline | Informatik |
| edition | Als Ms. gedr. |
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| spelling | Kaiser, Markus Verfasser (DE-588)141940425 aut Computer verification of algorithms using a formal proof system vorgelegt von Markus Kaiser Als Ms. gedr. Berlin dissertation.de 2010 198 S. graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier dissertation.de 1583 Zugl.: Darmstadt, Techn. Univ., Diss., 2009 Public-Key-Kryptosystem (DE-588)4209133-0 gnd rswk-swf Formale Semantik (DE-588)4122144-8 gnd rswk-swf Formale Spezifikationstechnik (DE-588)4299725-2 gnd rswk-swf Beweissystem (DE-588)4711800-3 gnd rswk-swf HOL (DE-588)4335765-9 gnd rswk-swf Verifikation (DE-588)4135577-5 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Verifikation (DE-588)4135577-5 s Formale Spezifikationstechnik (DE-588)4299725-2 s HOL (DE-588)4335765-9 s Formale Semantik (DE-588)4122144-8 s Beweissystem (DE-588)4711800-3 s Public-Key-Kryptosystem (DE-588)4209133-0 s DE-604 dissertation.de 1583 (DE-604)BV021464926 1583 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020684609&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kaiser, Markus Computer verification of algorithms using a formal proof system dissertation.de Public-Key-Kryptosystem (DE-588)4209133-0 gnd Formale Semantik (DE-588)4122144-8 gnd Formale Spezifikationstechnik (DE-588)4299725-2 gnd Beweissystem (DE-588)4711800-3 gnd HOL (DE-588)4335765-9 gnd Verifikation (DE-588)4135577-5 gnd |
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| title | Computer verification of algorithms using a formal proof system |
| title_auth | Computer verification of algorithms using a formal proof system |
| title_exact_search | Computer verification of algorithms using a formal proof system |
| title_full | Computer verification of algorithms using a formal proof system vorgelegt von Markus Kaiser |
| title_fullStr | Computer verification of algorithms using a formal proof system vorgelegt von Markus Kaiser |
| title_full_unstemmed | Computer verification of algorithms using a formal proof system vorgelegt von Markus Kaiser |
| title_short | Computer verification of algorithms using a formal proof system |
| title_sort | computer verification of algorithms using a formal proof system |
| topic | Public-Key-Kryptosystem (DE-588)4209133-0 gnd Formale Semantik (DE-588)4122144-8 gnd Formale Spezifikationstechnik (DE-588)4299725-2 gnd Beweissystem (DE-588)4711800-3 gnd HOL (DE-588)4335765-9 gnd Verifikation (DE-588)4135577-5 gnd |
| topic_facet | Public-Key-Kryptosystem Formale Semantik Formale Spezifikationstechnik Beweissystem HOL Verifikation Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020684609&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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