Codes: an introduction to information communication and cryptography
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London
Springer
2008
|
| Series: | Springer undergraduate mathematics series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 273 S. graph. Darst. |
| ISBN: | 1848002726 9781848002722 |
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| 245 | 1 | 0 | |a Codes |b an introduction to information communication and cryptography |c Norman L. Biggs |
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Record in the Search Index
| _version_ | 1804137779448250368 |
|---|---|
| adam_text | Contents
Preface
.........................................................
v
1.
Coding and its uses
......................................... 1
1.1
Messages
................................................ 1
1.2
Coding
.................................................. 3
1.3
Bask; definitions
.......................................... 4
1.4
Coding for economy
...................................... 7
1.5
Coding for reliability
...................................... 8
1.6
Coding for security
....................................... 9
2.
Prefix-free codes
............................................ 13
2.1
The decoding problem
.................................... 13
2.2
Representing codes by trees
................................ 16
2.3
The Kraft-McMillan number
............................... 18
2.4
Unique decodability implies
К
<
.......................... 21
2.5
Proof of the Counting Principle
............................ 24
3.
Economical coding
.......................................... 27
3.1
The concept of a source
................................... 27
3.2
The optimization problem
................................. 30
3.3
Entropy
................................................. 32
3.4
Entropy, uncertainty, and information
....................... 34
3.5
Optimal codes the fundamental theorems
.................. 38
3.6
Huffman s rule
........................................... 40
3.7
Optimality of Huffman codes
............................... 44
4.
Data compression
........................................... 47
4.1
Coding in blocks
......................................... 47
4.2
Distributions on product sets
.............................. 49
4.3
Stationary sources
........................................ 52
4.4
Coding a stationary source
................................ 55
4.5
Algorithms for data compression
........................... 58
4.6
Using numbers as codewords
............................... 59
4.7
Arithmetic coding
........................................ 62
4.8
The properties of arithmetic coding
......................... 65
4.9
Coding with a dynamic dictionary
.......................... 67
5.
Noisy channels
.............................................. 73
5.1
The definition of a channel
................................ 73
5.2
Transmitting a source through a channel
.................... 76
5.3
Conditional entropy
...................................... 78
5.4
The capacity of a channel
................................. 81
5.5
Calculating the capacity of a channel
....................... 83
6.
The problem of reliable communication
..................... 89
6.1
Communication using a noisy channel
....................... 89
6.2
The extended
BSC ....................................... 94
6.3
Decision rules
............................................ 96
6.4
Error correction
..........................................100
6.5
The packing bound
.......................................102
7.
The noisy coding theorems
.................................107
7.1
The probability of a mistake
...............................107
7.2
Coding at a given rate
....................................
Ill
7.3
Transmission using the extended
BSC.......................113
7.4
The rate should not exceed the capacity
.....................117
7.5
Shannon s theorem
.......................................119
7.6
Proof of
Fano
s
inequality
.................................120
8.
Linear codes
................................................123
8.1
Introduction to linear codes
................................123
8.2
Construction of linear codes using matrices
..................126
8.3
The check matrix of a linear code
...........................128
8.4
Constructing l-error-correcting codes
.......................131
8.5
Tho decoding problem
....................................135
Contents
¡χ
9.
Algebraic coding theory
....................................141
9.1
Hamming codes
..........................................141
9.2
Cyclic codes
.............................................145
9.3
Classification and properties of cyclic codes
..................149
9.4
Codes that can correct more than one error
..................153
9.5
Definition of a family of BCH codes
.........................155
9.6
Properties of the BCH codes
...............................158
10.
Coding natural languages
...................................163
10.1
Natural languages as sources
...............................163
10.2
The uncertainty of english
................................165
10.3
Redundancy and meaning
.................................168
10.4
Introduction to cryptography
..............................170
10.5
Frequency analysis
........................................174
11.
The development of cryptography
..........................179
11.1
Symmetric, key cryptosystems
..............................179
11.2
Poly-alphabetic encryption
................................180
11.3
The
Playfair
system
......................................183
11.4
Mathematical algorithms in cryptography
...................185
11.5
Methods of attack
........................................187
12.
Cryptography in theory and practice
.......................191
12.1
Encryption in terms of a channel
...........................191
12.2
Perfect secrecy
...........................................195
12.3
The one-time pad
........................................197
12.4
Iterative methods
.........................................198
12.5
Encryption standards
.....................................201
12.6
The key distribution problem
..............................203
13.
The RSA
cryptoSystem
.....................................207
13.1
A new approach to cryptography
...........................207
13.2
Outline of the RSA system
................................209
13.3
Feasibility of RSA
........................................212
13.4
Correctness of RSA
.......................................215
13.5
Confidentiality of RSA
....................................217
14.
Cryptography and calculation
..............................221
14.1
The scope of cryptography
.................................221
14.2
Hashing
.................................................222
14.3
Calculations in the field ¥p
................................224
14.4
The discrete logarithm
....................................226
14.5
The ElGamal cryptosystem
................................228
14.6
The Diffie-Hellman key distribution system
..................230
14.7
Signature schemes
........................................232
15.
Elliptic curve cryptography
.................................287
15.1
Calculations in finite groups
...............................237
15.2
The general ElGamal cryptosystem
.........................239
15.3
Elliptic curves
............................................241
15.4
The group of an elliptic curve
..............................245
15.5
Improving the efficiency of exponentiation
...................248
15.6
A final word
.............................................250
Answers to odd-numbered exercises
............................255
Index
...........................................................271
|
| adam_txt |
Contents
Preface
.
v
1.
Coding and its uses
. 1
1.1
Messages
. 1
1.2
Coding
. 3
1.3
Bask; definitions
. 4
1.4
Coding for economy
. 7
1.5
Coding for reliability
. 8
1.6
Coding for security
. 9
2.
Prefix-free codes
. 13
2.1
The decoding problem
. 13
2.2
Representing codes by trees
. 16
2.3
The Kraft-McMillan number
. 18
2.4
Unique decodability implies
К
<\
. 21
2.5
Proof of the Counting Principle
. 24
3.
Economical coding
. 27
3.1
The concept of a source
. 27
3.2
The optimization problem
. 30
3.3
Entropy
. 32
3.4
Entropy, uncertainty, and information
. 34
3.5
Optimal codes the fundamental theorems
. 38
3.6
Huffman's rule
. 40
3.7
Optimality of Huffman codes
. 44
4.
Data compression
. 47
4.1
Coding in blocks
. 47
4.2
Distributions on product sets
. 49
4.3
Stationary sources
. 52
4.4
Coding a stationary source
. 55
4.5
Algorithms for data compression
. 58
4.6
Using numbers as codewords
. 59
4.7
Arithmetic coding
. 62
4.8
The properties of arithmetic coding
. 65
4.9
Coding with a dynamic dictionary
. 67
5.
Noisy channels
. 73
5.1
The definition of a channel
. 73
5.2
Transmitting a source through a channel
. 76
5.3
Conditional entropy
. 78
5.4
The capacity of a channel
. 81
5.5
Calculating the capacity of a channel
. 83
6.
The problem of reliable communication
. 89
6.1
Communication using a noisy channel
. 89
6.2
The extended
BSC . 94
6.3
Decision rules
. 96
6.4
Error correction
.100
6.5
The packing bound
.102
7.
The noisy coding theorems
.107
7.1
The probability of a mistake
.107
7.2
Coding at a given rate
.
Ill
7.3
Transmission using the extended
BSC.113
7.4
The rate should not exceed the capacity
.117
7.5
Shannon's theorem
.119
7.6
Proof of
Fano
s
inequality
.120
8.
Linear codes
.123
8.1
Introduction to linear codes
.123
8.2
Construction of linear codes using matrices
.126
8.3
The check matrix of a linear code
.128
8.4
Constructing l-error-correcting codes
.131
8.5
Tho decoding problem
.135
Contents
¡χ
9.
Algebraic coding theory
.141
9.1
Hamming codes
.141
9.2
Cyclic codes
.145
9.3
Classification and properties of cyclic codes
.149
9.4
Codes that can correct more than one error
.153
9.5
Definition of a family of BCH codes
.155
9.6
Properties of the BCH codes
.158
10.
Coding natural languages
.163
10.1
Natural languages as sources
.163
10.2
The uncertainty of english
.165
10.3
Redundancy and meaning
.168
10.4
Introduction to cryptography
.170
10.5
Frequency analysis
.174
11.
The development of cryptography
.179
11.1
Symmetric, key cryptosystems
.179
11.2
Poly-alphabetic encryption
.180
11.3
The
Playfair
system
.183
11.4
Mathematical algorithms in cryptography
.185
11.5
Methods of attack
.187
12.
Cryptography in theory and practice
.191
12.1
Encryption in terms of a channel
.191
12.2
Perfect secrecy
.195
12.3
The one-time pad
.197
12.4
Iterative methods
.198
12.5
Encryption standards
.201
12.6
The key distribution problem
.203
13.
The RSA
cryptoSystem
.207
13.1
A new approach to cryptography
.207
13.2
Outline of the RSA system
.209
13.3
Feasibility of RSA
.212
13.4
Correctness of RSA
.215
13.5
Confidentiality of RSA
.217
14.
Cryptography and calculation
.221
14.1
The scope of cryptography
.221
14.2
Hashing
.222
14.3
Calculations in the field ¥p
.224
14.4
The discrete logarithm
.226
14.5
The ElGamal cryptosystem
.228
14.6
The Diffie-Hellman key distribution system
.230
14.7
Signature schemes
.232
15.
Elliptic curve cryptography
.287
15.1
Calculations in finite groups
.237
15.2
The general ElGamal cryptosystem
.239
15.3
Elliptic curves
.241
15.4
The group of an elliptic curve
.245
15.5
Improving the efficiency of exponentiation
.248
15.6
A final word
.250
Answers to odd-numbered exercises
.255
Index
.271 |
| any_adam_object | 1 |
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| author | Biggs, Norman 1941- |
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| classification_rvk | SK 170 ST 276 |
| ctrlnum | (OCoLC)226976116 (DE-599)DNB988023849 |
| dewey-full | 003.54 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 003 - Systems |
| dewey-raw | 003.54 |
| dewey-search | 003.54 |
| dewey-sort | 13.54 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| discipline_str_mv | Informatik Mathematik |
| format | Book |
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| index_date | 2024-07-02T21:22:44Z |
| indexdate | 2024-07-09T21:17:43Z |
| institution | BVB |
| isbn | 1848002726 9781848002722 |
| language | English |
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| spelling | Biggs, Norman 1941- Verfasser (DE-588)136105580 aut Codes an introduction to information communication and cryptography Norman L. Biggs London Springer 2008 X, 273 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer undergraduate mathematics series Coding theory Cryptography Codierungstheorie (DE-588)4139405-7 gnd rswk-swf Kryptologie (DE-588)4033329-2 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Kryptologie (DE-588)4033329-2 s DE-604 Codierungstheorie (DE-588)4139405-7 s Erscheint auch als Online-Ausgabe 978-1-84800-273-9 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016580896&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Biggs, Norman 1941- Codes an introduction to information communication and cryptography Coding theory Cryptography Codierungstheorie (DE-588)4139405-7 gnd Kryptologie (DE-588)4033329-2 gnd |
| subject_GND | (DE-588)4139405-7 (DE-588)4033329-2 (DE-588)4151278-9 |
| title | Codes an introduction to information communication and cryptography |
| title_auth | Codes an introduction to information communication and cryptography |
| title_exact_search | Codes an introduction to information communication and cryptography |
| title_exact_search_txtP | Codes an introduction to information communication and cryptography |
| title_full | Codes an introduction to information communication and cryptography Norman L. Biggs |
| title_fullStr | Codes an introduction to information communication and cryptography Norman L. Biggs |
| title_full_unstemmed | Codes an introduction to information communication and cryptography Norman L. Biggs |
| title_short | Codes |
| title_sort | codes an introduction to information communication and cryptography |
| title_sub | an introduction to information communication and cryptography |
| topic | Coding theory Cryptography Codierungstheorie (DE-588)4139405-7 gnd Kryptologie (DE-588)4033329-2 gnd |
| topic_facet | Coding theory Cryptography Codierungstheorie Kryptologie Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016580896&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT biggsnorman codesanintroductiontoinformationcommunicationandcryptography |