Galois fields, linear feedback shift registers and their applications: with 85 illustrations as well as numerous tables, diagrams and examples
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
München
Fachbuchverlag Leipzig im Carl Hanser Verlag
[2018]
|
| Schlagworte: | |
| Online-Zugang: | http://www.hanser-fachbuch.de/9783446451407 Inhaltsverzeichnis |
| Beschreibung: | 180 Seiten Diagramme 24 cm |
| ISBN: | 9783446451407 3446451404 |
Internformat
MARC
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|---|---|---|---|
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| 100 | 1 | |a Jetzek, Ulrich |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Galois fields, linear feedback shift registers and their applications |b with 85 illustrations as well as numerous tables, diagrams and examples |c Ulrich Jetzek |
| 264 | 1 | |a München |b Fachbuchverlag Leipzig im Carl Hanser Verlag |c [2018] | |
| 264 | 4 | |c © 2018 | |
| 300 | |a 180 Seiten |b Diagramme |c 24 cm | ||
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| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a LFSR |0 (DE-588)4472929-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Galois-Feld |0 (DE-588)4155896-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kryptologie |0 (DE-588)4033329-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Satellitennavigation |0 (DE-588)4202846-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Zyklische Redundanzprüfung |0 (DE-588)7746301-8 |2 gnd |9 rswk-swf |
| 653 | |a Cryptography | ||
| 653 | |a m sequence | ||
| 653 | |a Navigaton system | ||
| 653 | |a Prime field | ||
| 653 | |a MABA2018 | ||
| 689 | 0 | 0 | |a LFSR |0 (DE-588)4472929-7 |D s |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-030495421 | ||
Datensatz im Suchindex
| _version_ | 1804178740840759296 |
|---|---|
| adam_text | CONTENTS
0
INTRODUCTION.....................................................................................
13
0
FINITE GROUPS AND
FIELDS................................................................
17
2.1 MODULAR
ARITHMETIC.............................................................................
18
2.2 GROUPS, RINGS AND
FIELDS.....................................................................
20
2.3 GALOIS
FIELDS.......................................................................................
23
2.3.1 PRIME FIELDS
...............................................................................
25
2.3.1.1 EXISTENCE OF PRIME
FIELDS.............................................. 25
2.3.1.2 GENERATORS OF PRIME FIELDS
...........................................
27
2.3.1.3 MULTIPLICATIVE INVERSES IN PRIME FIELDS
........................
28
2.3.1.4 CYCLIC STRUCTURE OF PRIME FIELDS
....................................
29
2.3.2 EXTENSION
FIELDS.........................................................................
31
2.3.2.1 EXISTENCE OF EXTENSION FIELDS
........................................
32
2.3.2.2 IRREDUCIBLE
POLYNOMIALS................................................. 33
2.3.2.3 MODULAR ARITHMETIC OVER POLYNOMIALS.......................... 36
2.3.2.4 PRIMITIVE OR GENERATOR POLYNOMIALS..............................
37
2.4 LESSONS
LEARNED..................................................................................
41
2.5
EXERCISES..............................................................................................
43
0
WORKING WITH EXTENSION FIELDS
......................................................
45
3.1 PRIMITIVE POLYNOMIAL REPRESENTATIONS
...............................................
45
3.2 ADDITION OVER EXTENSION
FIELDS........................................................... 47
3.3 MULTIPLICATION OVER EXTENSION
FIELDS.................................................. 49
3.3.1 MULTIPLICATION IN POLYNOMIAL FORM
...........................................
49
3.3.2 MULTIPLICATION BY MEANS OF STRING REPRESENTATION
....................
50
3.3.3 MULTIPLICATION USING THE PRIMITIVE POLYNOMIAL
........................
51
3.4 MULTIPLICATIVE INVERSE WITHIN EXTENSION FIELDS
...................................
52
3.5 LESSONS
LEARNED..................................................................................
54
3.6
EXERCISES..............................................................................................
55
Q LINEAR FEEDBACK SHIFT
REGISTERS.................................................... 59
4.1 RING
COUNTERS......................................................................................
60
4.2 JOHNSON
COUNTERS................................................................................
61
4.3 DESIGN OF LINEAR FEEDBACK SHIFT REGISTERS BASED ON GALOIS FIELD
THEORY.................................................................................................
63
4.3.1 DESIGN OF LINEAR FEEDBACK SHIFT REGISTER CIRCUITS
BASED ON PRIMITIVE POLYNOMIALS
...............................................
64
4.3.2 LFSRS BASED ON IRREDUCIBLE (NON-PRIMITIVE) POLYNOMIALS
.......
67
4.3.3 LFSRS BASED ON REDUCIBLE POLYNOMIALS
....................................
70
4.4 FURTHER TOPICS RELATED TO LINEAR FEEDBACK SHIFT REGISTERS
....................
72
4.4.1 CHECKING IF A SPECIFIC POLYNOMIAL IS PRIMITIVE,
IRREDUCIBLE OR
REDUCIBLE....................................................... 72
4.4.2 A SYSTEMATIC WAY OF HOW TO DETERMINE PRIMITIVE POLYNOMIALS . 76
4.5 LESSONS
LEARNED..................................................................................
78
4.6
EXERCISES..............................................................................................
79
Q CORRELATION FUNCTIONS AND PSEUDO-RANDOM SEQUENCES
............
81
5.1 CORRELATION
FUNCTIONS.........................................................................
84
5.2 MAXIMUM LENGTH SEQUENCES (M-SEQUENCES)
....................................
89
5.3 REAL RANDOM SEQUENCES AND THEIR PROPERTIES
...................................
91
5.4 PROPERTIES OF
M-SEQUENCES.................................................................
92
5.5 LESSONS
LEARNED..................................................................................
93
5.6
EXERCISES..............................................................................................
94
Q APPLICATIONS OF GALOIS FIELDS AND LINEAR FEEDBACK SHIFT
R
EGISTERS..........................................................................................
97
6.1 LFSRS WITHIN THE GLOBAL POSITIONING SYSTEM (GPS)
............................
97
6.1.1 THE POSITIONING PRINCIPLE OF
GPS.............................................. 98
6.1.2 GPS
CODES..................................................................................
99
6.1.3 C/A-CODE GENERATION WITHIN THE GLOBAL POSITIONING SYSTEM
(GPS)..........................................................................................
100
6.1.4 P-CODE GENERATION WITHIN THE GLOBAL POSITIONING SYSTEM
.......
105
6.2 DATA TRANSMISSION IN
GPS..................................................................
110
6.2.1 THE SPREADING PRINCIPLE
.....................
112
6.3 LFSRS IN GALILEO
..............................................................................
119
6.3.1 MOTIVATION BEHIND GALILEO
....................................................
119
6.3.2 HISTORY OF GALILEO
...................................................................
121
6.3.3 GALILEO
SERVICES......................................................................
122
6.3.4 GALILEO AND GPS COMPARISON
................................................
125
6.3.5 GALILEO OPEN-SERVICE (OS) SYSTEM CODES
...............................
125
6.4 LFSR APPLICATIONS IN CRYPTOGRAPHY
...................................................
132
6.4.1 A5/1- A STREAM CIPHER USED IN
GSM.......................................... 137
6.4.2
TRIVIUM......................................................................................
140
6.5 CYCLIC REDUNDANCY CHECKS (CRC) USING
LFSRS.................................. 141
6.5.1 THE CORE IDEA OF
CRC................................................................. 141
6.5.2 THE MATHEMATICAL DESCRIPTION OF
CRC...................................... 142
6.5.3 IMPLEMENTATION ASPECTS OF CRC
...............................................
148
6.5.4 OPTIMIZING CRC-CALCULATION
....................................................
151
6.6 LESSONS
LEARNED..................................................................................
155
6.7
EXERCISES..............................................................................................
157
Q APPENDIX
.........................................................................................
159
7.1 PROBLEM
SOLUTIONS..............................................................................
159
7.1.1 SOLUTIONS TO PROBLEMS IN CHAPTER 2
.......................................... 159
7.1.2 SOLUTIONS TO PROBLEMS IN CHAPTER 3
.......................................... 161
7.1.3 SOLUTIONS TO PROBLEMS IN CHAPTER 4
.......................................... 165
7.1.4 SOLUTIONS TO PROBLEMS IN CHAPTER 5
.......................................... 169
7.1.5 SOLUTIONS TO PROBLEMS IN CHAPTER 6
.......................................... 171
7.2 LIST OF PRIMITIVE AND IRREDUCIBLE POLYNOMIALS
....................................
171
INDEX
179
|
| any_adam_object | 1 |
| author | Jetzek, Ulrich |
| author_facet | Jetzek, Ulrich |
| author_role | aut |
| author_sort | Jetzek, Ulrich |
| author_variant | u j uj |
| building | Verbundindex |
| bvnumber | BV045104933 |
| classification_rvk | SK 200 |
| ctrlnum | (OCoLC)1047415835 (DE-599)DNB1148580034 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| isbn | 9783446451407 3446451404 |
| language | English |
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| physical | 180 Seiten Diagramme 24 cm |
| publishDate | 2018 |
| publishDateSearch | 2018 |
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| publisher | Fachbuchverlag Leipzig im Carl Hanser Verlag |
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| spelling | Jetzek, Ulrich Verfasser aut Galois fields, linear feedback shift registers and their applications with 85 illustrations as well as numerous tables, diagrams and examples Ulrich Jetzek München Fachbuchverlag Leipzig im Carl Hanser Verlag [2018] © 2018 180 Seiten Diagramme 24 cm txt rdacontent n rdamedia nc rdacarrier LFSR (DE-588)4472929-7 gnd rswk-swf Galois-Feld (DE-588)4155896-0 gnd rswk-swf Kryptologie (DE-588)4033329-2 gnd rswk-swf Satellitennavigation (DE-588)4202846-2 gnd rswk-swf Zyklische Redundanzprüfung (DE-588)7746301-8 gnd rswk-swf Cryptography m sequence Navigaton system Prime field MABA2018 LFSR (DE-588)4472929-7 s Galois-Feld (DE-588)4155896-0 s Satellitennavigation (DE-588)4202846-2 s Kryptologie (DE-588)4033329-2 s Zyklische Redundanzprüfung (DE-588)7746301-8 s DE-604 X:MVB http://www.hanser-fachbuch.de/9783446451407 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030495421&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jetzek, Ulrich Galois fields, linear feedback shift registers and their applications with 85 illustrations as well as numerous tables, diagrams and examples LFSR (DE-588)4472929-7 gnd Galois-Feld (DE-588)4155896-0 gnd Kryptologie (DE-588)4033329-2 gnd Satellitennavigation (DE-588)4202846-2 gnd Zyklische Redundanzprüfung (DE-588)7746301-8 gnd |
| subject_GND | (DE-588)4472929-7 (DE-588)4155896-0 (DE-588)4033329-2 (DE-588)4202846-2 (DE-588)7746301-8 |
| title | Galois fields, linear feedback shift registers and their applications with 85 illustrations as well as numerous tables, diagrams and examples |
| title_auth | Galois fields, linear feedback shift registers and their applications with 85 illustrations as well as numerous tables, diagrams and examples |
| title_exact_search | Galois fields, linear feedback shift registers and their applications with 85 illustrations as well as numerous tables, diagrams and examples |
| title_full | Galois fields, linear feedback shift registers and their applications with 85 illustrations as well as numerous tables, diagrams and examples Ulrich Jetzek |
| title_fullStr | Galois fields, linear feedback shift registers and their applications with 85 illustrations as well as numerous tables, diagrams and examples Ulrich Jetzek |
| title_full_unstemmed | Galois fields, linear feedback shift registers and their applications with 85 illustrations as well as numerous tables, diagrams and examples Ulrich Jetzek |
| title_short | Galois fields, linear feedback shift registers and their applications |
| title_sort | galois fields linear feedback shift registers and their applications with 85 illustrations as well as numerous tables diagrams and examples |
| title_sub | with 85 illustrations as well as numerous tables, diagrams and examples |
| topic | LFSR (DE-588)4472929-7 gnd Galois-Feld (DE-588)4155896-0 gnd Kryptologie (DE-588)4033329-2 gnd Satellitennavigation (DE-588)4202846-2 gnd Zyklische Redundanzprüfung (DE-588)7746301-8 gnd |
| topic_facet | LFSR Galois-Feld Kryptologie Satellitennavigation Zyklische Redundanzprüfung |
| url | http://www.hanser-fachbuch.de/9783446451407 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030495421&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT jetzekulrich galoisfieldslinearfeedbackshiftregistersandtheirapplicationswith85illustrationsaswellasnumeroustablesdiagramsandexamples |