Elementary number theory, cryptography and codes:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2009
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | BTU01 TUM01 UBA01 UBM01 UBT01 UER01 UPA01 Volltext Inhaltsverzeichnis |
| Physical Description: | 1 Online-Ressource |
| ISBN: | 9783540692003 |
| DOI: | 10.1007/978-3-540-69200-3 |
Staff View
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Record in the Search Index
| _version_ | 1804139005009199104 |
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| adam_text | CL PROGRAMMING EXERCISES 84 CONTENTS A ROUND-UP 011 NUMBERS 1 1.1
MATHEINATICAL INDUETION 1 1.2 THE COIIFCPT OF RECURSION 5 1.2.1
FIHONACCI NUMBERS G 1.2.2 FURT HER EXANIPLES OF POPULATION DYNAMICS 11
1.2.3 THE TOWER OF HANOI: A NON-HONIOGENEOUS LINEAR CASE .... 13 1.3 THE
EUDIDEAN ALGORITHIN 14 1.3.1 DIVISION 14 1.3.2 THE GREATEST EOMMON
DIVISOR L(I 1.3.3 BEZOUT S IDENTITY 17 1.3.4 LINEAR DIOPHANTINE
EQUATIONS 20 1.3.5 EUCLIDEAN RINGS 21 1.3.0 POLYNOMIALS 23 1.4 COUNTING
IN DIFFERENT HASES 3(1 1.4.1 POSITIONAL NOTATION OF MNNHERS 30 1.4.2
BASE 2 32 1.4.3 THE FOUR OPERATIONS IN BASE 2 33 1.4.4 INTEGER MNNBERS
IN AN ARBITRARY BASE 39 1.4.5 REPRESENTATION OF REAL NUNIBERS IN AN
ARBITRARY BASE .... 40 1.5 CONTINUED FRACTIONS 43 1.5.1 FINITE SIMPLE
CONTINUED FRACTIONS AND RATIONAL NUNIBERS . 44 1.5.2 INFINITE SIMPLE
CONTINUED FRACTIONS AND IRRATIONAL NUNIBERS 48 1.5.3 PERIODIE CONTINUED
FRACTIONS 5( 1.5.4 A GEOMETRICAL MODEL FOR EONTINUED FRAETKMS 57 1.5.5
THE APPROXINIATION OF IRRATIONAL NUMBERS BY CONVERGENTS 58 1.5.(
CONTINUED FRACTIONS AND DIOPHANTINE EQUATIONS 01 APPENDIX TO CHAPTER 1
62 AI THEORETICAL EXERRISES (I2 BL COMPUTATIONAL EXERCISES 73
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/991139887 DIGITALISIERT
DURCH XII CONTENTS 2 COMPUTATIONAL COMPLEXITY 87 2.1 THE IDEA OF
COMPUTATIONAL COMPLEXITY 87 2.2 THE SYMBOL O 89 2.3 POLYIIOINIAL THNE,
EXPONENTIAL TIME 92 2.4 COMPLEXITY OF ELEMENTARY OPERATIONS 95 2.5
ALGORITHMS AND COMPLEXITY 97 2.5.1 COMPLEXITY OF THE EUCLIDEAN ALGORITHM
98 2.5.2 FROM BINARY TO DECIMAL REPRESENTATION: COMPLEXITY 101 2.5.3
COMPLEXITY OF OPERATIONS ON POLYNOMIALS 101 2.5.4 A MORE EFFICIENT
MULTIPLICATION ALGORITHM 103 2.5.5 THE RUFFINI-HORNER METHOD 105
APPENDIX TO CHAPTER 2 107 A2 THEORETICAL EXERCISES 107 B2 COMPUTATIONAL
EXERCISES 109 C2 PROGRAMMING EXERCISES 113 3 FROM INFINITE TO FINITE 115
3.1 CONGRUENCE: FUNDAMENTAL PROPERTIES 115 3.2 ELEMENTARY APPLICATIONS
OF CONGRUENCE 120 3.2.1 CASTING OUT NINES 120 3.2.2 TESTS OF
DIVISIBILITY 121 3.3 LINEAR CONGRUENCES 122 3.3.1 POWERS MODULO N 126
3.4 THE CHINESE REMAINDER THEOREM 128 3.5 EXAMPLES 133 3.5.1 PERPETUA!
CALENDAR 133 3.5.2 ROUND-ROBIN TOURNAMENTS 136 APPENDIX TO CHAPTER 3 136
A3 THEORETICAL EXERCISES 136 B3 COMPUTATIONAL EXERCISES 140 C3
PROGRAMMING EXERCISES 147 4 FINITE IS NOT ENOUGH: FACTORING INTEGERS 149
4.1 PRIME NUMBERS 149 4.1.1 THE FUNDAMENTAL THEOREM OF ARITHMETIC 150
4.1. CONTENTS XIII 4.4.3 MERSENNE PRIMES 172 4.4.4 PERFECT NUNIBERS 173
4.5 FACTORISATION IN AN INTEGRAL DONIAIN 173 4.5.1 PRIME AND IRREDUCIBLE
ELEINENTS IN A RING 174 4.5.2 FACTORIAL DOMAINS 175 4.5.3 NOETHERIAN
RINGS 177 4.5.4 FACTORISATION OF POLYNONUEALS OVER A FIELD 179 4.5.5
FACTORISATION OF POLYNONIIALS OVER A FACTORIAL RING 182 4.5.6
POLYNONIIALS WITH RATIONAL OR INTEGER COEFFICIENTS 188 4.6 LAGRANGE
INTERPOLATION AND ITS APPLICATIONS 191 4.7 KRONECKER S FACTORISATION
METHOD 195 APPENDIX TO CHAPTER 4 198 A4 THEORETICAL EXERCISES 198 B4
COMPUTATIONAL EXERCISES 204 C4 PROGRAMMING EXERCISES 211 FINITE FIELDS
AND POLYNOMIAL CONGRUENCES 213 5.1 SOME FIELD THEORY 213 5.1.1 FIELD
EXTENSIONS 213 5.1.2 ALGEBRAIC EXTENSIONS 214 5.1.3 SPLITTING FIELD OF A
POLYNOMIAL 217 5.1.4 ROOTS OF UNITY 218 5.1.5 ALGEBRAIC CLOSURE 219
5.1.6 FINITE FIELDS AND THEIR SUBFIELDS 220 5.1.7 AUTOMORPHISNIS OF
FINITE FIELDS 222 5.1.8 IRREDUCIBLE POLYNONIIALS OVER Z P 222 5.1.9 THE
FIELD F 4 OF ORDER FOUR 224 5.1.10 THE FIELD F S OF ORDER EIGHT 225
5.1.11 THE FIELD F LFL OF ORDER SIXTEEN 226 5.1.12 THE FIELD F 9 OF
ORDER NINE 226 5.1.13 ABOUT THE GENERATORS OF A FINITE FIELD 227 5.1.1
XIV CONTENTS 6 PRIMALITY AND FACTORISATION TESTS 261 6.1 PSEUDOPRIME
NUMBERS AND PROBABILISTIC TESTS 261 6.1.1 PSEUDOPRINIE NUNIBERS 261
6.1.2 PROBABILISTIC TESTS AND DETERMINISTIE TESTS 263 6.1.3 A FIRST
PROBABILISTIC PRIMALITY TEST 263 6.1.4 CARMICHAEL NUNIBERS 264 6.1.5
EULER PSEUDOPRIINES 265 6.1.6 THE SOLOVAY-STRASSEN PROBABILISTIC
PRIMALITY TEST 268 6.1.7 STRONG PSEUDOPRIINES 268 6.1.8 THE MILLER-RABIN
PROBABILISTIC PRIMALITY TEST 272 6.2 PRIMITIVE ROOTS 273 6.2.1 PRIMITIVE
ROOTS AND INDEX 278 6.2.2 MORE ABOUT THE MILLER-RABIN TEST 279 6.3 A
POLYNOMIAL DETERMINISTIE PRIMALITY TEST 281 6.4 FACTORISATION METHODS
290 6.4.1 FERMAT FACTORISATION METHOD 291 6.4.2 GENERALISATION OF FERMAT
FACTORISATION METHOD 292 6.4.3 THE METHOD OF FACTOR BASES 294 6.4.4
FACTORISATION AND CONTINUED FRACTIONS 299 6.4.5 THE QUADRATIC SIEVE
ALGORITHM 300 6.4.6 THE P METHOD 309 6.4.7 VARIATION OF P METHOD 311
APPENDIX TO CHAPTER 6 313 A6 THEORETICAL EXERCISES 313 B6 COMPUTATIONAL
EXERCISES 315 C6 PROGRAMMING EXERCISES 317 7 SECRETS. .. AND LIES 319
7.1 THE CLASSIC CIPHERS 319 7.1.1 THE EARLIEST SECRET RUESSAGES IN
HISTORY 319 7.2 THE ANALYSIS OF THE CIPHERTEXT 325 7.2.1 ENCIPHERING
MACHINES 329 7.3 MATHEMATICAL SETTING OF A CRYPTOSYSTEM 330 7. CONTENTS
XV 7.7.4 WHY DID IT WORK? 356 7.7.5 AUTHENTICATION OF SIGNATURES WITH
THE RSA SYSTEM 360 7.7.6 A REMARK ABOUT THE SEEURITY OF RSA SYSTEM 362
7.8 VARIANTS OF RSA SYSTEM AND BEYOND 363 7.8.1 EXCHANGING PRIVATE KEYS
363 7.8.2 ELGAMAL CRYPTOSYSTEM 364 7.8.3 ZERO-KNOWLEDGE PROOF:
PERSUADING THAT A RESULT IS KNOWN WITHOUT REVEALING ITS CONTENT NOR ITS
PROOF 365 7.8.4 HISTORICAL NOTE 366 7.9 CRYPTOGRAPHY AND ELLIPTIC CURVES
366 7.9.1 CRYPTOGRAPHY IN A GROUP 367 7.9.2 ALGEBRAIC CURVES IN A
NUMERICAL AFFINE PLANE 368 7.9.3 LINES AND RATIONAL CURVES 369 7.9.4
HYPERELLIPTIC CURVES 370 7.9.5 ELLIPTIC CURVES 372 7.9.6 GROUP LAW ON
ELLIPTIC CURVES 374 7.9.7 ELLIPTIC CURVES OVER R. C AND Q 380 7.9.8
ELLIPTIC CURVES OVER FINITE FIELDS 381 7.9.9 ELLIPTIC CURVES AND
CRYPTOGRAPHY 384 7.9.10 POLLARD S P - 1 FACTORISATION METHOD 385
APPENDIX TO CHAPTER 7 386 A7 THEORETICAL EXERCISES 386 B7 COMPUTATIONAL
EXERCISES 390 C7 PROGRAMMING EXERCISES 401 TRANSMITTING WITHOUT... FEAR
OF ERRORS 405 8.1 BIRTHDAY GREETINGS 406 8.2 TAKING PHOTOS IN SPACE OR
TOSSING COINS. WE END UP AT CODES . . . 407 8.3 ERROR-CORRECTING CODES
410 8.4 BOUNDS ON THE INVARIANTS 413 8. XVI CONTENTS A9 THEORETICAL
EXERCISES 467 B9 COMPUTATIONAL EXERCISES 468 C9 PROGRAMMING EXERCISES
469 SOLUTION TO SELECTED EXERCISES 471 EXERCISES OF CHAPTER 1 471
EXERCISES OF CHAPTER 2 482 EXERCISES OF CHAPTER 3 483 EXERCISES OF
CHAPTER 4 487 EXERCISES OF CHAPTER 5 492 EXERCISES OF CHAPTER 6 496
EXERCISES OF CHAPTER 7 498 EXERCISES OF CHAPTER 8 501 EXERCISES OF
CHAPTER 9 504 REFERENCES 507 INDEX 511
|
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| author | Baldoni, Maria Welleda 1949- Ciliberto, Ciro 1950- Piacentini Cattaneo, Giulia Maria |
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| dewey-full | 512.7 |
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7 |
| dewey-search | 512.7 |
| dewey-sort | 3512.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| doi_str_mv | 10.1007/978-3-540-69200-3 |
| format | Electronic eBook |
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| id | DE-604.BV023805391 |
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| indexdate | 2024-07-09T21:37:12Z |
| institution | BVB |
| isbn | 9783540692003 |
| language | English |
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| series2 | Universitext |
| spelling | Baldoni, Maria Welleda 1949- Verfasser (DE-588)124501001 aut Aritmetica, crittografia e codici Elementary number theory, cryptography and codes Maria Welleda Baldoni ; Ciro Ciliberto ; Giulia Maria Piacentini Cattaneo Berlin [u.a.] Springer 2009 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Universitext Code (DE-588)4010345-6 gnd rswk-swf Kryptologie (DE-588)4033329-2 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s Kryptologie (DE-588)4033329-2 s Code (DE-588)4010345-6 s DE-604 Ciliberto, Ciro 1950- Verfasser (DE-588)130563080 aut Piacentini Cattaneo, Giulia Maria Verfasser aut Erscheint auch als Druckausgabe 978-3-540-69199-0 https://doi.org/10.1007/978-3-540-69200-3 Verlag Volltext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017447566&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baldoni, Maria Welleda 1949- Ciliberto, Ciro 1950- Piacentini Cattaneo, Giulia Maria Elementary number theory, cryptography and codes Code (DE-588)4010345-6 gnd Kryptologie (DE-588)4033329-2 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4010345-6 (DE-588)4033329-2 (DE-588)4067277-3 |
| title | Elementary number theory, cryptography and codes |
| title_alt | Aritmetica, crittografia e codici |
| title_auth | Elementary number theory, cryptography and codes |
| title_exact_search | Elementary number theory, cryptography and codes |
| title_full | Elementary number theory, cryptography and codes Maria Welleda Baldoni ; Ciro Ciliberto ; Giulia Maria Piacentini Cattaneo |
| title_fullStr | Elementary number theory, cryptography and codes Maria Welleda Baldoni ; Ciro Ciliberto ; Giulia Maria Piacentini Cattaneo |
| title_full_unstemmed | Elementary number theory, cryptography and codes Maria Welleda Baldoni ; Ciro Ciliberto ; Giulia Maria Piacentini Cattaneo |
| title_short | Elementary number theory, cryptography and codes |
| title_sort | elementary number theory cryptography and codes |
| topic | Code (DE-588)4010345-6 gnd Kryptologie (DE-588)4033329-2 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Code Kryptologie Zahlentheorie |
| url | https://doi.org/10.1007/978-3-540-69200-3 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017447566&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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