Stream ciphers and number theory:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam [u.a.]
Elsevier
2004
|
| Ausgabe: | Rev. ed. |
| Schriftenreihe: | North-Holland mathematical library
55 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 474 S. |
| ISBN: | 044451631X |
Internformat
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| 245 | 1 | 0 | |a Stream ciphers and number theory |c Thomas W. Cusick ; Cunsheng Ding ; Ari Renvall |
| 250 | |a Rev. ed. | ||
| 264 | 1 | |a Amsterdam [u.a.] |b Elsevier |c 2004 | |
| 300 | |a XVII, 474 S. | ||
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Datensatz im Suchindex
| _version_ | 1804133106540609536 |
|---|---|
| adam_text | STREAM CIPHERS AND NUMBER THEORY REVISED EDITION THOMAS W. CUSICK THE
STATE UNIVERSITY OF NEW YORK AT BUFFALO, NY, U.S.A. CUNSHENG DING THE
HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY CHINA ARI RENVALL THE
UNIVERSITY OF TURKU FINLAND ELSEVIER 2004 AMSTERDAM - BOSTON -
HEIDELBERG - LONDON - NEW YORK - OXFORD PARIS - SAN DIEGO -SAN FRANCISCO
- SINGAPORE - SYDNEY - TOKYO CONTENTS PREFACE TO THE REVISED EDITION VII
PREFACE TO THE FIRST EDITION IX 1 INTRODUCTION 1 1.1 APPLICATIONS OF
NUMBER THEORY 2 1.2 AN OUTLINE OF THIS BOOK 5 2 STREAM CIPHERS 11 2.1
STREAM CIPHER SYSTEMS 11 2.1.1 ADDITIVE SYNCHRONOUS STREAM CIPHERS 13
2.1.2 ADDITIVE SELF-SYNCHRONOUS STREAM CIPHERS 14 2.1.3 NONADDITIVE
SYNCHRONOUS STREAM CIPHERS 14 2.1.4 STREAM CIPHERING WITH BLOCK CIPHERS
16 2.1.5 COOPERATIVELY DISTRIBUTED CIPHERING 18 2.2 SOME KEYSTREAM
GENERATORS 21 2.2.1 GENERATORS BASED ON COUNTERS 22 2.2.2 SOME
NUMBER-THEORETIC GENERATORS 24 2.3 CRYPTOGRAPHIC ASPECTS OF SEQUENCES 25
2.3.1 MINIMAL POLYNOMIAL AND LINEAR COMPLEXITY 25 2.3.2 PATTERN
DISTRIBUTION OF KEY STREAMS 29 2.3.3 CORRELATION FUNCTIONS 31 2.3.4
SPHERE COMPLEXITY AND LINEAR CRYPTANALYSIS 33 2.3.5 HIGHER ORDER
COMPLEXITIES 36 2.4 HARMONY OF BINARY NSGS 37 2.5 SECURITY AND ATTACKS
41 3 PRIMES, PRIMITIVE ROOTS AND SEQUENCES 45 3.1 CYCLOTOMIC POLYNOMIALS
45 3.2 TWO BASIC PROBLEMS FROM STREAM CIPHERS 47 XI XII CONTENTS 3.3 A
BASIC THEOREM AND MAIN BRIDGE 50 3.4 PRIMES, PRIMITIVE ROOTS AND BINARY
SEQUENCES 53 3.5 PRIMES, PRIMITIVE ROOTS AND TERNARY SEQUENCES 58 3.6
PRIMES, NEGORD AND SEQUENCES 61 3.7 PRIME POWERS, PRIMITIVE ROOTS AND
SEQUENCES 63 3.8 PRIME PRODUCTS AND SEQUENCES 65 3.8.1 BINARY SEQUENCES
AND PRIMES 66 3.8.2 TERNARY SEQUENCES AND PRIMES 67 3.9 ON CRYPTOGRAPHIC
PRIMITIVE ROOTS 68 3.10 LINEAR COMPLEXITY OF SEQUENCES OVER Z M 70 3.11
PERIOD AND ITS CRYPTOGRAPHIC IMPORTANCE 79 3.12 RECENT ADVANCES ON THE
SPHERE COMPLEXITY 80 4 CYCLOTOMY AND CRYPTOGRAPHIC FUNCTIONS 83 4.1
CYCLOTOMIC NUMBERS 83 4.2 CYCLOTOMY AND CRYPTOGRAPHY 85 4.2.1 CYCLOTOMY
AND DIFFERENCE PARAMETERS 86 4.2.2 CYCLOTOMY AND THE DIFFERENTIAL
CRYPTANALYSIS 87 4.2.3 CRYPTOGRAPHIC CYCLOTOMIC NUMBERS 88 4.3
CRYPTOGRAPHIC FUNCTIONS FROM Z P TO Z& 89 4.3.1 THE CASE D = 2 91 4.3.2
THE CASE D = 3 92 4.3.3 THE CASE D = 4 93 4.3.4 THE CASE D = 5 94 4.3.5
THE CASE D = 6 96 4.3.6 THE CASE D = 8 96 4.3.7 THE CASE D = 10 99 4.3.8
THE CASE D = 12 100 4.4 CRYPTOGRAPHIC FUNCTIONS FROM Z PQ TO ZD 101
4.4.1 WHITEMAN S GENERALIZED CYCLOTOMY AND CRYPTOGRAPHY 101 4.4.2
CRYPTOGRAPHIC FUNCTIONS FROM Z PG TO ZI 107 4.4.3 CRYPTOGRAPHIC
FUNCTIONS FROM Z VQ TO Z 110 4.5 CRYPTOGRAPHIC FUNCTIONS FROM Z P I TO
ZI ILL 4.6 CRYPTOGRAPHIC FUNCTIONS DEFINED ON GF(P M ) 115 4.7 THE
ORIGIN OF CYCLOTOMIC NUMBERS 115 5 SPECIAL PRIMES AND SEQUENCES 121 5.1
SOPHIE GERMAIN PRIMES AND SEQUENCES 121 5.1.1 THEIR IMPORTANCE IN STREAM
CIPHERS 122 5.1.2 THEIR RELATIONS WITH OTHER NUMBER-THEORETIC
PROBLEMSL23 5.1.3 THE EXISTENCE PROBLEM 124 5.1.4 A SEARCH FOR
CRYPTOGRAPHIC SOPHIE GERMAIN PRIMES . 124 CONTENTS XIII 5.2 TCHEBYCHEF
PRIMES AND SEQUENCES 126 5.2.1 THEIR CRYPTOGRAPHIC SIGNIFICANCE 126
5.2.2 EXISTENCE AND SEARCH PROBLEM 126 5.3 OTHER PRIMES OF FORM FC X 2 N
+ 1 AND SEQUENCES 127 5.4 PRIMES OF FORM (O N * L)/(O * 1) AND SEQUENCES
131 5.4.1 MERSENNE PRIMES AND SEQUENCES 132 5.4.2 CRYPTOGRAPHIC PRIMES
OF FORM ((4U) N - L)/(4W - 1) . 134 5.4.3 PRIME REPUNITS AND THEIR
CRYPTOGRAPHIC VALUES . . . 135 5.5 N 1 AND P# 1 PRIMES AND
SEQUENCES 136 5.6 TWIN PRIMES AND SEQUENCES OVER GF(2) 138 5.6.1 THE
SIGNIFICANCE OF TWINS AND THEIR SEXES 138 5.6.2 CRYPTOGRAPHIC TWINS AND
THE SEX DISTRIBUTION . . . . 140 5.7 TWIN PRIMES AND SEQUENCES OVER
GF(3) 142 5.8 OTHER SPECIAL PRIMES AND SEQUENCES 143 5.9 PRIME
DISTRIBUTIONS AND THEIR SIGNIFICANCE 143 5.10 PRIMES FOR STREAM CIPHERS
AND FOR RSA 144 6 HIGHLY NONLINEAR FUNCTIONS 147 6.1 PRELIMINARIES 148
6.2 FUNCTIONS WITH PERFECT NONLINEARITY 149 6.2.1 STABILITY OF THE SET
OF PERFECT NONLINEAR FUNCTIONS UN- DER ACTIONS OF GENERAL AFFINE GROUPS
150 6.2.2 PERFECT NONLINEAR FUNCTIONS AND DIFFERENCE PARTITIONS . 151
6.2.3 FUNCTIONS WITH PERFECT NONLINEARITY AND DIFFERENCE MA- TRICES 155
6.2.4 A CHARACTERIZATION OF PERFECT NONLINEARITY BY MEANS OF FOURIER
TRANSFORM 156 6.2.5 OBTAINING FUNCTIONS WITH PERFECT NONLINEARITY FROM
KNOWN ONES 159 6.2.6 BENT FUNCTIONS AND PERFECT NONLINEARITY 161 6.3
BINARY FUNCTIONS WITH OPTIMUM NONLINEARITY 162 6.3.1 THE CASE N = 0 (MOD
4) 163 6.3.2 THE CASE N = 3 (MOD 4) 165 6.3.3 THE CASE N = 2 (MOD 4) 166
6.3.4 THE CASE N = 1 (MOD 4) AND N 1 170 6.3.5 MINIMUM DISTANCE FROM
ARBNE FUNCTIONS 172 6.4 NONBINARY FUNCTIONS WITH OPTIMUM NONLINEARITY
173 6.4.1 THE CASE B = 3 173 6.4.2 THE CASE |B|=4 174 6.5
CONSTRUCTIONS OF FUNCTIONS WITH OPTIMUM NONLINEARITY . . . . 176 6.5.1
FUNCTIONS FROM {GF{Q) N ,+) TO (GF(Q),+) 176 XIV CONTENTS 6.5.2
FUNCTIONS FROM (GF(Q) N ,+) TO (GF(Q) N ,+): PERFECT AND ALMOST PERFECT
NONLINEAR MAPPINGS 179 6.5.3 FUNCTIONS WITH OPTIMUM NONLINEARITY FROM
LINEAR FUNCTIONS 181 6.5.4 OTHER FUNCTIONS FROM (GF(2 M )*,X) TO
(GF(2),+) WITH OPTIMUM NONLINEARITY 181 6.5.5 FUNCTIONS FROM ZJ TO Z Q
183 7 DIFFERENCE SETS AND SEQUENCES 185 7.1 THE NSG REALIZATION OF
SEQUENCES 185 7.2 DIFFERENTIAL ANALYSIS OF SEQUENCES 187 7.3 LINEAR
COMPLEXITY OF DSC (ADSC) SEQUENCES 189 7.4 BARKER SEQUENCES 192 8 BINARY
CYCLOTOMIC GENERATORS 195 8.1 CYCLOTOMIC GENERATOR OF ORDER 2K 195 8.2
TWO-PRIME GENERATOR OF ORDER 2 198 8.3 TWO-PRIME GENERATOR OF ORDER 4
212 8.4 PRIME-SQUARE GENERATOR 213 8.5 IMPLEMENTATION AND PERFORMANCE
225 8.6 A SUMMARY OF BINARY CYCLOTOMIC GENERATORS 225 9 ANALYSIS OF
CYCLOTOMIC GENERATORS OF ORDER 2 227 9.1 CROSSCORRELATION PROPERTY 228
9.2 DECIMATION PROPERTY 229 9.3 LINEAR COMPLEXITY 229 9.4 SECURITY
AGAINST A DECISION TREE ATTACK 233 9.5 SUMS OF DSC SEQUENCES 247 9.5.1
LINEAR COMPLEXITY ANALYSIS 248 9.5.2 BALANCE ANALYSIS 248 9.5.3
CORRELATION ANALYSIS 249 9.5.4 DIFFERENTIAL ANALYSIS 249 10 NONBINARY
CYCLOTOMIC GENERATORS 251 10.1 THE RTH-ORDER CYCLOTOMIC GENERATOR 251
10.2 LINEAR COMPLEXITY 252 10.3 AUTOCORRELATION PROPERTY 255 10.4
DECIMATION PROPERTY 256 10.5 IDEAS BEHIND THE CYCLOTOMIC GENERATORS 257
CONTENTS XV 11 GENERATORS BASED ON PERMUTATIONS 259 11.1 THE
CRYPTOGRAPHIC IDEA 259 11.2 PERMUTATIONS ON FINITE FIELDS 261 11.2.1
DICKSON PERMUTATION POLYNOMIALS 262 11.2.2 LINEARIZED PERMUTATION
POLYNOMIALS 262 11.2.3 PERMUTATION POLYNOMIALS OF THE FORM X (Q+RN-I)/M
+ AX 262 11.2.4 PERMUTATION POLYNOMIALS OF THE FORM X R (G{X 8 ))( Q -
1)/S 262 11.2.5 COHEN PERMUTATION POLYNOMIALS 263 11.3 A GENERATOR BASED
ON INVERSE PERMUTATIONS 263 11.4 BINARY GENERATORS AND PERMUTATIONS OF
GF(2 N ) 264 11.4.1 APN PERMUTATIONS AND THEIR PROPERTIES 266 11.4.2
QUADRATIC PERMUTATIONS WITH CONTROLLABLE NONLINEARITY270 11.4.3
PERMUTATIONS OF ORDER 3 272 11.4.4 APN PERMUTATIONS OF ORDER N - 1 273
11.4.5 PERMUTATIONS OF ORDER N - 2 274 11.4.6 PERMUTATIONS X D WITH D =
2 M - 1 275 11.4.7 APN PERMUTATIONS VIA CROSSCORRELATION FUNCTION . . .
276 11.4.8 OTHER POWER FUNCTIONS WITH GOOD NONLINEARITY .... 280 11.4.9
CHOOSING THE LINEAR FUNCTIONS 280 11.5 CYCLIC-KEY GENERATORS AND THEIR
PROBLEMS 281 11.5.1 CYCLIC-KEY GENERATORS 281 11.5.2 SEVERAL SPECIFIC
FORMS: AN OVERVIEW 284 11.6 A GENERATOR BASED ON PERMUTATIONS OF Z M 286
12 QUADRATIC PARTITIONS AND CRYPTOGRAPHY 295 12.1 QUADRATIC PARTITION
AND CRYPTOGRAPHY 296 12.2 P = X 2 + Y 2 AND P = X 2 + 4Y 2 297 12.3 P =
X 2 + 2Y 2 AND P = X 2 + 3Y 2 304 12.4 P = X 2 + NY 2 AND QUADRATIC
RECIPROCITY 305 12.5 P = X 2 + 7Y 2 AND QUADRATIC FORMS 306 12.6 P = X 2
+ 15Y 2 AND GENUS THEORY 310 12.7 P = X 2 + NY 2 AND CLASS FIELD THEORY
311 12.8 OTHER CRYPTOGRAPHIC QUADRATIC PARTITIONS 314 13 GROUP
CHARACTERS AND CRYPTOGRAPHY 317 13.1 GROUP CHARACTERS 317 13.2 FIELD
CHARACTERS AND CRYPTOGRAPHY 319 13.2.1 FIELD MULTIPLICATIVE CHARACTERS:
MOST USED ONES . . . 321 13.2.2 FIELD ADDITIVE CHARACTERS: MOST USED
ONES 323 13.3 GROUP CHARACTERS AND CYCLOTOMIC NUMBERS 329 13.4 THE
NONLINEARITY OF CHARACTERS 333 13.4.1 THE NONLINEARITY OF MULTIPLICATIVE
CHARACTERS 333 XVI CONTENTS 13.4.2 THE NONLINEARITY OF ADDITIVE
CHARACTERS 335 13.5 RING CHARACTERS AND CRYPTOGRAPHY 335 14 P-ADIC
NUMBERS, CLASS NUMBERS AND SEQUENCES 337 14.1 THE 2-ADIC VALUE AND
2-ADIC EXPANSION 337 14.2 A FAST ALGORITHM FOR THE 2-ADIC EXPANSION 343
14.3 THE ARITHMETIC OF Q [2 ] AND Z [2 ] 343 14.4 FEEDBACK SHIFT
REGISTERS WITH CARRY 349 14.5 ANALYSIS AND SYNTHESIS OF FCSRS 351 14.6
THE 2-ADIC SPAN AND 2-RA ALGORITHM 356 14.7 SOME PROPERTIES OF FCSR
SEQUENCES 366 14.8 BLUM-BLUM-SHUB SEQUENCES & CLASS NUMBERS 370 15 PRIME
CIPHERING ALGORITHMS 379 15.1 PRIME-32: A DESCRIPTION 379 15.2
THEORETICAL RESULTS ABOUT PRIME-32 385 15.3 SECURITY ARGUMENTS 386 15.4
PERFORMANCE OF PRIME-32 389 15.5 PRIME-32 WITH A 192-BIT KEY 389 15.6
PRIME-64 389 16 CRYPTOGRAPHIC PROBLEMS AND PHILOSOPHIES 391 16.1
NONLINEARITY AND LINEARITY 391 16.2 STABILITY AND INSTABILITY 394 16.2.1
STABILITY AND DIFFUSION 395 16.2.2 CORRELATION STABILITY AND PATTERN
STABILITY 397 16.2.3 MUTUAL INFORMATION STABILITY 397 16.3 LOCALNESS AND
GLOBALNESS 399 16.4 GOODNESS AND BADNESS 400 16.5 ABOUT GOOD PLUS GOOD
401 16.6 ABOUT GOOD PLUS BAD 403 16.7 ABOUT BAD PLUS GOOD 403 16.8
HARDWARE AND SOFTWARE MODEL COMPLEXITY 404 APPENDICES 407 A MORE ABOUT
CYCLOTOMIC NUMBERS 407 A.I CYCLOTOMIC NUMBERS OF ORDER 7 407 A.2
CYCLOTOMIC NUMBERS OF ORDERS 9, 18 409 A.3 CYCLOTOMIC NUMBERS OF ORDER
ELEVEN 410 A.4 ON OTHER CYCLOTOMIC NUMBERS 411 A.5 BEHIND CYCLOTOMIC
NUMBERS 411 CONTENTS XVU B CYCLOTOMIC FORMULAE OF ORDERS 6, 8 AND 10 C
FINDING PRACTICAL PRIMES D LIST OF RESEARCH PROBLEMS E EXERCISES F LIST
OF MATHEMATICAL SYMBOLS BIBLIOGRAPHY INDEX 415 423 425 429 435 437 472
|
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| id | DE-604.BV019672235 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T20:03:27Z |
| institution | BVB |
| isbn | 044451631X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013000428 |
| oclc_num | 249960775 |
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| owner_facet | DE-91G DE-BY-TUM DE-522 |
| physical | XVII, 474 S. |
| publishDate | 2004 |
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| publisher | Elsevier |
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| series | North-Holland mathematical library |
| series2 | North-Holland mathematical library |
| spelling | Cusick, Thomas W. Verfasser aut Stream ciphers and number theory Thomas W. Cusick ; Cunsheng Ding ; Ari Renvall Rev. ed. Amsterdam [u.a.] Elsevier 2004 XVII, 474 S. txt rdacontent n rdamedia nc rdacarrier North-Holland mathematical library 55 Stromchiffre - Zahlentheorie Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Stromchiffre (DE-588)4271270-1 gnd rswk-swf Stromchiffre (DE-588)4271270-1 s Zahlentheorie (DE-588)4067277-3 s DE-604 Ding, Cunsheng 1962- Verfasser (DE-588)121230457 aut Renvall, Ari Verfasser aut North-Holland mathematical library 55 (DE-604)BV000005206 55 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013000428&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cusick, Thomas W. Ding, Cunsheng 1962- Renvall, Ari Stream ciphers and number theory North-Holland mathematical library Stromchiffre - Zahlentheorie Zahlentheorie (DE-588)4067277-3 gnd Stromchiffre (DE-588)4271270-1 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4271270-1 |
| title | Stream ciphers and number theory |
| title_auth | Stream ciphers and number theory |
| title_exact_search | Stream ciphers and number theory |
| title_full | Stream ciphers and number theory Thomas W. Cusick ; Cunsheng Ding ; Ari Renvall |
| title_fullStr | Stream ciphers and number theory Thomas W. Cusick ; Cunsheng Ding ; Ari Renvall |
| title_full_unstemmed | Stream ciphers and number theory Thomas W. Cusick ; Cunsheng Ding ; Ari Renvall |
| title_short | Stream ciphers and number theory |
| title_sort | stream ciphers and number theory |
| topic | Stromchiffre - Zahlentheorie Zahlentheorie (DE-588)4067277-3 gnd Stromchiffre (DE-588)4271270-1 gnd |
| topic_facet | Stromchiffre - Zahlentheorie Zahlentheorie Stromchiffre |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013000428&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005206 |
| work_keys_str_mv | AT cusickthomasw streamciphersandnumbertheory AT dingcunsheng streamciphersandnumbertheory AT renvallari streamciphersandnumbertheory |