A primer on pseudorandom generators:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2010
|
| Series: | University lecture series
55 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | X, 114 S. graph. Darst. |
| ISBN: | 9780821851920 |
Staff View
MARC
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| 100 | 1 | |a Goldreich, Oded |d 1957- |e Verfasser |0 (DE-588)120549255 |4 aut | |
| 245 | 1 | 0 | |a A primer on pseudorandom generators |c Oded Goldreich |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2010 | |
| 300 | |a X, 114 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
їх
1
Introduction
1
1.1
The Third Theory of Randomness
.................... 2
1.2
Organization of the Primer
........................ 4
1.3
Standard Conventions
........................... 5
1.4
The General Paradigm
........................... 6
1.4.1
Three fundamental aspects
.................... 6
1.4.2
Notational conventions
....................... 7
1.4.3
Some instantiations of the general paradigm
........... 8
Notes
....................................... 8
Exercises
..................................... 9
2
General-Purpose Pseudorandom Generators
11
2.1
The Basic Definition
............................ 11
2.2
The Archetypical Application
....................... 12
2.3
Computational Indistinguishability
.................... 15
2.3.1
The general formulation
...................... 15
2.3.2
Relation to statistical closeness
.................. 16
2.3.3
Indistinguishability by multiple samples
............. 16
2.4
Amplifying the Stretch Function
..................... 19
2.5
Constructions
................................ 21
2.5.1
Background: one-way functions
.................. 21
2.5.2
A simple construction
....................... 23
2.5.3
An alternative presentation
.................... 23
2.5.4
A necessary and sufficient condition
............... 24
2.6
Non-uniformly Strong Pseudorandom Generators
............ 25
2.7
Stronger (Uniform-Complexity) Notions
................. 27
2.7.1
Fooling stronger distinguishers
.................. 27
2.7.2
Pseudorandom functions
...................... 27
2.8
Conceptual Reflections
........................... 29
Notes
....................................... 30
Exercises
..................................... 31
vi
CONTENTS
3 Derandomization
of Time-Complexity Classes
35
3.1
Denning Canonical Derandomizers
.................... 35
3.2
Constructing Canonical Derandomizers
.................. 37
3.2.1
The construction and its consequences
.............. 38
3.2.2
Analyzing the construction
.................... 40
3.2.3
Construction
3.4
as a general framework
............. 41
3.3
Reflections Regarding Derandomization
................. 43
Notes
....................................... 43
Exercises
..................................... 44
4
Space-Bounded Distinguishers
47
4.1
Definitional Issues
............................. 47
4.2
Two Constructions
............................. 50
4.2.1
Sketches of the proofs of Theorems
4.2
and
4.3......... 51
4.2.2
Derandomization of space-complexity classes
.......... 54
Notes
....................................... 56
Exercises
..................................... 56
5
Special Purpose Generators
59
5.1
Pairwise Independence Generators
.................... 60
5.1.1
Constructions
............................ 60
5.1.2
A taste of the applications
..................... 62
5.2
Small-Bias Generators
........................... 63
5.2.1
Constructions
............................ 64
5.2.2
A taste of the applications
..................... 65
5.2.3
Generalization
........................... 66
5.3
Random Walks on Expanders
....................... 66
5.3.1
Background: expanders and random walks on them
...... 67
5.3.2
The generator
............................ 68
Notes
....................................... 69
Exercises
..................................... 69
Concluding Remarks
77
Appendices
79
A Hashing Functions
79
A.I Definitions
.................................. 79
A.2 Constructions
................................80
A.3 The Leftover Hash Lemma
.........................81
В
On Randomness Extractors
83
B.I Definitions
..................................84
B.2 Constructions
................................85
CONTENTS
vii
С
A Generic
Hard-Core Predicate
89
D
Using Randomness in Computation
93
D.I A Simple Probabilistic Polynomial-Time Primality Test
........ 93
D.2 Testing Polynomial Identity
........................ 95
D.3 The Accidental Tourist Sees It All
.................... 96
E
Cryptographic Applications of Pseudorandom Functions
99
E.I Secret Communication
...........................99
E.2 Authenticated Communication
......................101
F
Some Basic Complexity Classes
103
Bibliography
107
Index
113
|
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| id | DE-604.BV036722116 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:46:36Z |
| institution | BVB |
| isbn | 9780821851920 |
| language | English |
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| physical | X, 114 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | University lecture series |
| series2 | University lecture series |
| spelling | Goldreich, Oded 1957- Verfasser (DE-588)120549255 aut A primer on pseudorandom generators Oded Goldreich Providence, RI American Math. Soc. 2010 X, 114 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier University lecture series 55 Includes bibliographical references and index Hausdorff-Maß (DE-588)4159238-4 gnd rswk-swf Quasikonforme Abbildung (DE-588)4199279-9 gnd rswk-swf Quasikonforme Abbildung (DE-588)4199279-9 s Hausdorff-Maß (DE-588)4159238-4 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1650-8 University lecture series 55 (DE-604)BV004153846 55 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020639969&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Goldreich, Oded 1957- A primer on pseudorandom generators University lecture series Hausdorff-Maß (DE-588)4159238-4 gnd Quasikonforme Abbildung (DE-588)4199279-9 gnd |
| subject_GND | (DE-588)4159238-4 (DE-588)4199279-9 |
| title | A primer on pseudorandom generators |
| title_auth | A primer on pseudorandom generators |
| title_exact_search | A primer on pseudorandom generators |
| title_full | A primer on pseudorandom generators Oded Goldreich |
| title_fullStr | A primer on pseudorandom generators Oded Goldreich |
| title_full_unstemmed | A primer on pseudorandom generators Oded Goldreich |
| title_short | A primer on pseudorandom generators |
| title_sort | a primer on pseudorandom generators |
| topic | Hausdorff-Maß (DE-588)4159238-4 gnd Quasikonforme Abbildung (DE-588)4199279-9 gnd |
| topic_facet | Hausdorff-Maß Quasikonforme Abbildung |
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