Fundamentals of cryptography: introducing mathematical and algorithmic foundations
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| Format: | Buch |
| Sprache: | English |
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Cham, Switzerland
Springer
[2021]
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| Schriftenreihe: | Undergraduate topics in computer science
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xv, 278 Seiten Illustrationen, Diagramme |
| ISBN: | 9783030734916 |
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| 100 | 1 | |a Buell, Duncan A. |d 1950- |e Verfasser |0 (DE-588)1069614254 |4 aut | |
| 245 | 1 | 0 | |a Fundamentals of cryptography |b introducing mathematical and algorithmic foundations |c Duncan Buell |
| 264 | 1 | |a Cham, Switzerland |b Springer |c [2021] | |
| 264 | 4 | |c © 2021 | |
| 300 | |a xv, 278 Seiten |b Illustrationen, Diagramme | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Undergraduate topics in computer science | |
| 650 | 4 | |a Systems and Data Security | |
| 650 | 4 | |a Cryptology | |
| 650 | 4 | |a Theory of Computation | |
| 650 | 4 | |a Computer security | |
| 650 | 4 | |a Data encryption (Computer science) | |
| 650 | 4 | |a Computers | |
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Datensatz im Suchindex
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| adam_text | Contents 1 Introduction................................................................................................ 1.1 History............................................................................................... 1.2 Introduction..................................................................................... 1.3 Why Is Cryptography Used?......................................................... 1.4 Modes of Encryption....................................................................... 1.5 Modes of Attack.............................................................................. 1.6 How Many Seconds ina Year?...................................................... 1.7 Kerckhoffs’ Principle........................................................................ 1.8 Exercises.......................................................................................... References..................................................................................................... 1 1 3 5 6 7 7 9 9 10 2 Simple Ciphers............................................................................................ 2.1 Substitution Ciphers........................................................................ 2.1.1 Caesar Ciphers.................................................................. 2.1.2 Random Substitutions....................................................... 2.1.3 Vigenère as an Example of Polyalphabetic Substitutions...................................................................... 2.2 Language Characteristics and
Patterns......................................... 2.2.1 Letter Frequency .............................................................. 2.2.2 Word Boundaries.............................................................. 2.2.3 Cribbing.............................................................................. 2.2.4 Entropy.............................................................................. 2.3 Transposition Ciphers..................................................................... 2.3.1 Columnar Transpositions.................................................. 2.3.2 Double Transposition ....................................................... 2.4 Playfair............................................................................................... 2.5 ADFGX............................................................................................. 2.6 Cryptanalysis.................................................................................... 2.6.1 Breaking a Substitution Cipher....................................... 2.6.2 Breaking a Transposition Cipher..................................... 2.7 The Vernam One-Time Pad............................................................ 11 12 12 12 13 14 14 15 16 16 19 19 20 20 21 22 22 23 23 ix
x Contents Exercises............................................................................................ 2.8.1 Cipher Text for Substitution Cipher Problems (3) and (4).................................................................. References...................................................................................................... 24 Divisibility,Congruences, and Modular Arithmetic............................. 3.1 Divisibility......................................................................................... 3.2 The Euclidean Algorithm.................................................................. 3.2.1 The Naive Euclidean Algorithm.................................... 3.2.2 The Extended Euclidean Algorithm............................... 3.2.3 The Binary Euclidean Algorithm.................................... 3.2.4 The Subtract-Three-Times Euclidean Algorithm.......... 3.2.5 GCDs of Large Integers.................................................. 3.3 Primes................................................................................................ 3.4 Congruences....................................................................................... 3.5 The Euler Totient............................................................................. 3.6 Fermat’s Little Theorem.................................................................. 3.7 Exponentiation.................................................................................. 3.8 Matrix Reduction.............................................................................. 3.9
Exercises........................................................................................... References...................................................................................................... 27 27 29 30 31 32 33 34 35 36 43 43 44 45 46 47 4 Groups, Rings, Fields................................................................................... 4.1 Groups................................................................................................. 4.2 Rings................................................................................................... 4.3 Fields................................................................................................... 4.4 Examples and Expansions................................................................ 4.4.1 Arithmetic Modulo Prime Numbers............................... 4.4.2 Arithmetic Modulo Composite Numbers..................... 4.4.3 Finite Fields of Characteristic 2...................................... 4.5 Exercises.......................................................................................... References..................................................................................................... 49 49 53 54 54 54 57 60 60 61 5 63 63 65 67 67 68 68 69 70 71 2.8 3 Square Roots and Quadratic Symbols..................................................... 5.1 Square Roots................................................................................... 5.1.1 Examples............................................................................ 5.2 Characters on
Groups..................................................................... 5.3 Legendre Symbols............................................................................. 5.4 Quadratic Reciprocity..................................................................... 5.5 Jacobi Symbols................................................................................. 5.6 Extended Law of Quadratic Reciprocity....................................... 5.7 Exercises........................................................................................... Reference....................................................................................................... 25 26
Contents xi 6 Finite Fieldsof Characteristic 2............................................................... 6.1 Polynomials with Coefficients mod 2........................................... 6.1.1 An Example...................................................................... 6.2 Linear Feedback Shift Registers.................................................... 6.3 The General Theory....................................................................... 6.4 Normal Bases................................................................................... 6.5 Exercises.......................................................................................... References..................................................................................................... 73 73 73 75 79 80 85 85 7 Elliptic Curves........................................................................................... 7.1 Basics .............................................................................................. 7.1.1 Straight Lines andIntersections........................................ 7.1.2 Tangent Lines................................... 7.1.3 Formulas............................................................................ 7.1.4 The Mordell-Weil Group................................................. 7.2 Observation..................................................................................... 7.3 Projective Coordinates and Jacobian Coordinates...................... 7.4 An Example of a Curve with Many Points.................................. 7.5 Curves Modulo a Prime
p.............................................................. 7.6 Hasse’s Theorem.............................................................................. 7.7 Exercises.......................................................................................... Reference....................................................................................................... 87 87 88 90 90 91 93 94 94 96 96 97 98 8 Mathematics, Computing,and Arithmetic............................................... 8.1 Mersenne Primes.............................................................................. 8.1.1 Introduction....................................................................... 8.1.2 Theory................................................................................. 8.1.3 Implementation................................................................... 8.1.4 Summary: Feasibility....................................................... 8.1.5 Fermat Numbers................................................................ 8.1.6 The Arithmetic Trick Is Important.................................. 8.2 Multiprecise Arithmetic and the Fast Fourier Transform........... 8.2.1 Multiprecise Arithmetic..................................................... 8.2.2 Background of the FFT..................................................... 8.2.3 Polynomial Multiplication................................................ 8.2.4 Complex Numbers as Needed forFourier Transforms......................................................................... 8.2.5 The Fourier
Transform..................................................... 8.2.6 The Cooley-Tukey Fast Fourier Transform.................. 8.2.7 An Example........................................................................ 8.2.8 The FFT Butterfly........................................................... 8.3 Montgomery Multiplication........................................................... 8.3.1 The Computational Advantage ...................................... 8.4 Arithmetic in General.................................................................... 99 99 100 100 103 104 104 105 105 105 106 106 107 108 109 110 116 117 120 120
xii Contents 8.5 Exercises........................................................................................... 120 References....................................................................................................... 121 Modem Symmetric Ciphers—DES and AES...................................... 9.1 History................................................................................................ 9.1.1 Criticism and Controversy............................................... 9.2 The Advanced Encryption Standard.............................................. 9.3 The AES Algorithm......................................................................... 9.3.1 Polynomial Preliminaries: The Galois Field GF(28)...................................................... 127 9.3.2 Byte Organization.............................................................. 9.4 The Structure of AES....................................................................... 9.4.1 The Outer Structure of the Rounds............................... 9.4.2 General Code Details........................................................ 9.4.3 KeyExpansion.................................................................... 9.4.4 SubBytes............................................................................. 9.4.5 ShiftRows........................................................................... 9.4.6 MixColumns...................................................................... 9.4.7 AddRoundKey................................................................. 9.5 Implementation
Issues..................................................................... 9.5.1 Software Implementations................................................. 9.5.2 Hardware Implementations.............................................. 9.6 Security.............................................................................................. 9.7 Exercises............................................................................................ References...................................................................................................... 9 123 123 124 125 127 128 129 129 129 130 133 136 137 140 141 142 144 145 146 147 10 Asymmetric Ciphers—RSA and Others............................................... 10.1 History................................................................................................ 10.2 RSA Public-Key Encryption.......................................................... 10.2.1 The Basic RSA Algorithm............................................. 10.3 Implementation.................................................................................. 10.3.1 An Example....................................................................... 10.4 How Hard Is It to Break RSA?...................................................... 10.5 Other Groups.................................................................................... 10.6 Exercises............................................................................................ References.....................................................................................................
149 149 150 150 151 152 153 153 155 155 11 How to Factor a Number......................................................................... 11.1 Pollard rho....................................................................................... 11.2 Pollard p ֊ 1 ..................................................................................... 11.2.1 The General Metaphysics of p - 1................................. 11.2.2 Step Two of p — 1........................................................... 157 158 160 161 161
Contents 12 11.3 CFRAC............................................................................................ 11.3.1 Continued Fractions........................................................ 11.3.2 The CFRAC Algorithm.................................................... 11.3.3 Example............................................................................. 11.3.4 Computation...................................................................... 11.4 Factoring with Elliptic Curves....................................................... 11.5 Exercises.......................................................................................... References..................................................................................................... 162 162 165 167 168 169 170 170 How to Factor More Effectively................................................................ 173 173 173 174 Shortcomings of CFRAC............................................................... The Quadratic Sieve...................................................................... 12.2.1 The Algorithm................................................................. 12.2.2 The Crucial Reasons for Success and Improvement over CFRAC..................................... 12.3 Once More Unto the Breach........................................................ 12.4 The Multiple Polynomial Quadratic Sieve................................... 12.4.1 Yet One More Advantage............................................. 12.5 The Number Field
Sieve............................................................... 12.6 Exercises......................................................................................... References.................................................................................................... 12.1 12.2 13 xiii Cycles, Randomness, Discrete Logarithms, andKey Exchange. ... Introduction..................................................................................... The Discrete Logarithm Problem.................................................. Difficult Discrete Log Problems..................................................... Cycles.............................................................................................. Cocks-Ellis-Williamson/Diffie-Hellman KeyExchange............... 13.5.1 The Key Exchange Algorithm....................................... 13.6 The Index Calculus......................................................................... 13.6.1 Our Example................................................................... 13.6.2 Smooth Relations............................................................ 13.6.3 Matrix Reduction............................................................ 13.6.4 Individual Logarithms..................................................... 13.6.5 Asymptotics..................................................................... 13.7 Key Exchange with Elliptic Curves.............................................. 13.8 Key Exchange in Other Groups..................................................... 13.9 How Hard Is the Discrete Logarithm
Problem?........................... 13.10 Exercises.......................................................................................... References..................................................................................................... 13.1 13.2 13.3 13.4 13.5 174 175 176 177 177 178 178 179 179 180 181 182 182 183 183 184 184 185 187 187 187 188 189 189 190
xiv Contents Elliptic Curve Cryptography...................................................................... 14.1 Introduction....................................................................................... 14.1.1 Jacobian Coordinates....................................................... 14.2 Elliptic Curve Discrete Logarithms................................................ 14.3 Elliptic Curve Cryptography........................................................... 14.4 The Cost of Elliptic Curve Operations......................................... 14.4.1 Doubling a Point............................................................... 14.4.2 Left-to-Right “Exponentiation”...................................... 14.5 The NIST Recommendations........................................................... 14.6 Attacks on Elliptic Curves................................................................ 14.6.1 Pohlig-Hellman Attacks .................................................. 14.6.2 Pollard Rho Attacks.......................................................... 14.6.3 Pollard Rho for Curves..................................................... 14.6.4 Pollard Rho in Parallel..................................................... 14.7 A Comparison of Complexities....................................................... 14.8 Exercises............................................................................................. References . ..................................................................................................... 14 191 191 192 193 193 194 194 195 196 198
198 198 200 201 202 202 202 Lattice-Based Cryptography and NTRU................................................ 15.1 Quantum Computing....................................................................... 15.2 Lattices: An Introduction ................................................................ 15.3 Hard Lattice Problems.................................................................... 15.4 NTRU.............................................................................................. 15.5 The NTRU Cryptosystem............................................................. 15.5.1 Parameters........................................................................ 15.5.2 Creating Keys ................................................................. 15.5.3 Encrypting a Message..................................................... 15.5.4 Decrypting a Message..................................................... 15.5.5 Why This Works............................................................. 15.5.6 Preventing Errors in Decryption................................... 15.6 Lattice Attacks on NTRU.............................................................. 15.7 The Mathematics of the Lattice Reduction Attack...................... 15.7.1 Other Attacks on NTRU.................................................. 15.7.2 Lattice Reduction............................................................. 15.8 NTRU Parameter Choices.............................................................. 15.9
Exercises.......................................................................................... References..................................................................................................... 205 205 207 208 209 210 210 211 211 211 213 213 214 216 217 217 218 220 220 16 Homomorphic Encryption......................................................................... 16.1 Introduction...................................................................................... 16.2 Somewhat Homomorphic Encryption............................................ 16.3 Fully Homomorphic Encryption..................................................... 16.4 Ideal Lattices.................................................................................... 16.5 Learning with Errors........................................................................ 223 223 224 224 224 227 15
Contents XV 16.6 Security, and Homomorphic Evaluation of Functions.............. 228 16.7 An Apologetic Summary............................................................... 228 References..................................................................................................... 228 Appendix A: An Actual World War I Cipher........................................... 231 Appendix B: AES Code.................................................................................... 253 Index..................................................................................................................... 275
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Contents 1 Introduction. 1.1 History. 1.2 Introduction. 1.3 Why Is Cryptography Used?. 1.4 Modes of Encryption. 1.5 Modes of Attack. 1.6 How Many Seconds ina Year?. 1.7 Kerckhoffs’ Principle. 1.8 Exercises. References. 1 1 3 5 6 7 7 9 9 10 2 Simple Ciphers. 2.1 Substitution Ciphers. 2.1.1 Caesar Ciphers. 2.1.2 Random Substitutions. 2.1.3 Vigenère as an Example of Polyalphabetic Substitutions. 2.2 Language Characteristics and
Patterns. 2.2.1 Letter Frequency . 2.2.2 Word Boundaries. 2.2.3 Cribbing. 2.2.4 Entropy. 2.3 Transposition Ciphers. 2.3.1 Columnar Transpositions. 2.3.2 Double Transposition . 2.4 Playfair. 2.5 ADFGX. 2.6 Cryptanalysis. 2.6.1 Breaking a Substitution Cipher. 2.6.2 Breaking a Transposition Cipher. 2.7 The Vernam One-Time Pad. 11 12 12 12 13 14 14 15 16 16 19 19 20 20 21 22 22 23 23 ix
x Contents Exercises. 2.8.1 Cipher Text for Substitution Cipher Problems (3) and (4). References. 24 Divisibility,Congruences, and Modular Arithmetic. 3.1 Divisibility. 3.2 The Euclidean Algorithm. 3.2.1 The Naive Euclidean Algorithm. 3.2.2 The Extended Euclidean Algorithm. 3.2.3 The Binary Euclidean Algorithm. 3.2.4 The Subtract-Three-Times Euclidean Algorithm. 3.2.5 GCDs of Large Integers. 3.3 Primes. 3.4 Congruences. 3.5 The Euler Totient. 3.6 Fermat’s Little Theorem. 3.7 Exponentiation. 3.8 Matrix Reduction. 3.9
Exercises. References. 27 27 29 30 31 32 33 34 35 36 43 43 44 45 46 47 4 Groups, Rings, Fields. 4.1 Groups. 4.2 Rings. 4.3 Fields. 4.4 Examples and Expansions. 4.4.1 Arithmetic Modulo Prime Numbers. 4.4.2 Arithmetic Modulo Composite Numbers. 4.4.3 Finite Fields of Characteristic 2. 4.5 Exercises. References. 49 49 53 54 54 54 57 60 60 61 5 63 63 65 67 67 68 68 69 70 71 2.8 3 Square Roots and Quadratic Symbols. 5.1 Square Roots. 5.1.1 Examples. 5.2 Characters on
Groups. 5.3 Legendre Symbols. 5.4 Quadratic Reciprocity. 5.5 Jacobi Symbols. 5.6 Extended Law of Quadratic Reciprocity. 5.7 Exercises. Reference. 25 26
Contents xi 6 Finite Fieldsof Characteristic 2. 6.1 Polynomials with Coefficients mod 2. 6.1.1 An Example. 6.2 Linear Feedback Shift Registers. 6.3 The General Theory. 6.4 Normal Bases. 6.5 Exercises. References. 73 73 73 75 79 80 85 85 7 Elliptic Curves. 7.1 Basics . 7.1.1 Straight Lines andIntersections. 7.1.2 Tangent Lines. 7.1.3 Formulas. 7.1.4 The Mordell-Weil Group. 7.2 Observation. 7.3 Projective Coordinates and Jacobian Coordinates. 7.4 An Example of a Curve with Many Points. 7.5 Curves Modulo a Prime
p. 7.6 Hasse’s Theorem. 7.7 Exercises. Reference. 87 87 88 90 90 91 93 94 94 96 96 97 98 8 Mathematics, Computing,and Arithmetic. 8.1 Mersenne Primes. 8.1.1 Introduction. 8.1.2 Theory. 8.1.3 Implementation. 8.1.4 Summary: Feasibility. 8.1.5 Fermat Numbers. 8.1.6 The Arithmetic Trick Is Important. 8.2 Multiprecise Arithmetic and the Fast Fourier Transform. 8.2.1 Multiprecise Arithmetic. 8.2.2 Background of the FFT. 8.2.3 Polynomial Multiplication. 8.2.4 Complex Numbers as Needed forFourier Transforms. 8.2.5 The Fourier
Transform. 8.2.6 The Cooley-Tukey Fast Fourier Transform. 8.2.7 An Example. 8.2.8 The FFT Butterfly. 8.3 Montgomery Multiplication. 8.3.1 The Computational Advantage . 8.4 Arithmetic in General. 99 99 100 100 103 104 104 105 105 105 106 106 107 108 109 110 116 117 120 120
xii Contents 8.5 Exercises. 120 References. 121 Modem Symmetric Ciphers—DES and AES. 9.1 History. 9.1.1 Criticism and Controversy. 9.2 The Advanced Encryption Standard. 9.3 The AES Algorithm. 9.3.1 Polynomial Preliminaries: The Galois Field GF(28). 127 9.3.2 Byte Organization. 9.4 The Structure of AES. 9.4.1 The Outer Structure of the Rounds. 9.4.2 General Code Details. 9.4.3 KeyExpansion. 9.4.4 SubBytes. 9.4.5 ShiftRows. 9.4.6 MixColumns. 9.4.7 AddRoundKey. 9.5 Implementation
Issues. 9.5.1 Software Implementations. 9.5.2 Hardware Implementations. 9.6 Security. 9.7 Exercises. References. 9 123 123 124 125 127 128 129 129 129 130 133 136 137 140 141 142 144 145 146 147 10 Asymmetric Ciphers—RSA and Others. 10.1 History. 10.2 RSA Public-Key Encryption. 10.2.1 The Basic RSA Algorithm. 10.3 Implementation. 10.3.1 An Example. 10.4 How Hard Is It to Break RSA?. 10.5 Other Groups. 10.6 Exercises. References.
149 149 150 150 151 152 153 153 155 155 11 How to Factor a Number. 11.1 Pollard rho. 11.2 Pollard p ֊ 1 . 11.2.1 The General Metaphysics of p - 1. 11.2.2 Step Two of p — 1. 157 158 160 161 161
Contents 12 11.3 CFRAC. 11.3.1 Continued Fractions. 11.3.2 The CFRAC Algorithm. 11.3.3 Example. 11.3.4 Computation. 11.4 Factoring with Elliptic Curves. 11.5 Exercises. References. 162 162 165 167 168 169 170 170 How to Factor More Effectively. 173 173 173 174 Shortcomings of CFRAC. The Quadratic Sieve. 12.2.1 The Algorithm. 12.2.2 The Crucial Reasons for Success and Improvement over CFRAC. 12.3 Once More Unto the Breach. 12.4 The Multiple Polynomial Quadratic Sieve. 12.4.1 Yet One More Advantage. 12.5 The Number Field
Sieve. 12.6 Exercises. References. 12.1 12.2 13 xiii Cycles, Randomness, Discrete Logarithms, andKey Exchange. . Introduction. The Discrete Logarithm Problem. Difficult Discrete Log Problems. Cycles. Cocks-Ellis-Williamson/Diffie-Hellman KeyExchange. 13.5.1 The Key Exchange Algorithm. 13.6 The Index Calculus. 13.6.1 Our Example. 13.6.2 Smooth Relations. 13.6.3 Matrix Reduction. 13.6.4 Individual Logarithms. 13.6.5 Asymptotics. 13.7 Key Exchange with Elliptic Curves. 13.8 Key Exchange in Other Groups. 13.9 How Hard Is the Discrete Logarithm
Problem?. 13.10 Exercises. References. 13.1 13.2 13.3 13.4 13.5 174 175 176 177 177 178 178 179 179 180 181 182 182 183 183 184 184 185 187 187 187 188 189 189 190
xiv Contents Elliptic Curve Cryptography. 14.1 Introduction. 14.1.1 Jacobian Coordinates. 14.2 Elliptic Curve Discrete Logarithms. 14.3 Elliptic Curve Cryptography. 14.4 The Cost of Elliptic Curve Operations. 14.4.1 Doubling a Point. 14.4.2 Left-to-Right “Exponentiation”. 14.5 The NIST Recommendations. 14.6 Attacks on Elliptic Curves. 14.6.1 Pohlig-Hellman Attacks . 14.6.2 Pollard Rho Attacks. 14.6.3 Pollard Rho for Curves. 14.6.4 Pollard Rho in Parallel. 14.7 A Comparison of Complexities. 14.8 Exercises. References . . 14 191 191 192 193 193 194 194 195 196 198
198 198 200 201 202 202 202 Lattice-Based Cryptography and NTRU. 15.1 Quantum Computing. 15.2 Lattices: An Introduction . 15.3 Hard Lattice Problems. 15.4 NTRU. 15.5 The NTRU Cryptosystem. 15.5.1 Parameters. 15.5.2 Creating Keys . 15.5.3 Encrypting a Message. 15.5.4 Decrypting a Message. 15.5.5 Why This Works. 15.5.6 Preventing Errors in Decryption. 15.6 Lattice Attacks on NTRU. 15.7 The Mathematics of the Lattice Reduction Attack. 15.7.1 Other Attacks on NTRU. 15.7.2 Lattice Reduction. 15.8 NTRU Parameter Choices. 15.9
Exercises. References. 205 205 207 208 209 210 210 211 211 211 213 213 214 216 217 217 218 220 220 16 Homomorphic Encryption. 16.1 Introduction. 16.2 Somewhat Homomorphic Encryption. 16.3 Fully Homomorphic Encryption. 16.4 Ideal Lattices. 16.5 Learning with Errors. 223 223 224 224 224 227 15
Contents XV 16.6 Security, and Homomorphic Evaluation of Functions. 228 16.7 An Apologetic Summary. 228 References. 228 Appendix A: An Actual World War I Cipher. 231 Appendix B: AES Code. 253 Index. 275 |
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| author | Buell, Duncan A. 1950- |
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| author_facet | Buell, Duncan A. 1950- |
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| ctrlnum | (OCoLC)1260122383 (DE-599)BVBBV047638109 |
| dewey-full | 005.8 |
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| discipline_str_mv | Informatik |
| format | Book |
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| id | DE-604.BV047638109 |
| illustrated | Illustrated |
| index_date | 2024-07-03T18:47:11Z |
| indexdate | 2024-07-10T09:17:54Z |
| institution | BVB |
| isbn | 9783030734916 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033022360 |
| oclc_num | 1260122383 |
| open_access_boolean | |
| owner | DE-11 DE-83 DE-703 DE-355 DE-BY-UBR |
| owner_facet | DE-11 DE-83 DE-703 DE-355 DE-BY-UBR |
| physical | xv, 278 Seiten Illustrationen, Diagramme |
| publishDate | 2021 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | Springer |
| record_format | marc |
| series2 | Undergraduate topics in computer science |
| spelling | Buell, Duncan A. 1950- Verfasser (DE-588)1069614254 aut Fundamentals of cryptography introducing mathematical and algorithmic foundations Duncan Buell Cham, Switzerland Springer [2021] © 2021 xv, 278 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Undergraduate topics in computer science Systems and Data Security Cryptology Theory of Computation Computer security Data encryption (Computer science) Computers Datensicherung (DE-588)4011144-1 gnd rswk-swf Kryptologie (DE-588)4033329-2 gnd rswk-swf Datensicherung (DE-588)4011144-1 s Kryptologie (DE-588)4033329-2 s DE-604 Erscheint auch als Online-Ausgabe 978-3-030-73492-3 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033022360&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Buell, Duncan A. 1950- Fundamentals of cryptography introducing mathematical and algorithmic foundations Systems and Data Security Cryptology Theory of Computation Computer security Data encryption (Computer science) Computers Datensicherung (DE-588)4011144-1 gnd Kryptologie (DE-588)4033329-2 gnd |
| subject_GND | (DE-588)4011144-1 (DE-588)4033329-2 |
| title | Fundamentals of cryptography introducing mathematical and algorithmic foundations |
| title_auth | Fundamentals of cryptography introducing mathematical and algorithmic foundations |
| title_exact_search | Fundamentals of cryptography introducing mathematical and algorithmic foundations |
| title_exact_search_txtP | Fundamentals of cryptography introducing mathematical and algorithmic foundations |
| title_full | Fundamentals of cryptography introducing mathematical and algorithmic foundations Duncan Buell |
| title_fullStr | Fundamentals of cryptography introducing mathematical and algorithmic foundations Duncan Buell |
| title_full_unstemmed | Fundamentals of cryptography introducing mathematical and algorithmic foundations Duncan Buell |
| title_short | Fundamentals of cryptography |
| title_sort | fundamentals of cryptography introducing mathematical and algorithmic foundations |
| title_sub | introducing mathematical and algorithmic foundations |
| topic | Systems and Data Security Cryptology Theory of Computation Computer security Data encryption (Computer science) Computers Datensicherung (DE-588)4011144-1 gnd Kryptologie (DE-588)4033329-2 gnd |
| topic_facet | Systems and Data Security Cryptology Theory of Computation Computer security Data encryption (Computer science) Computers Datensicherung Kryptologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033022360&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT buellduncana fundamentalsofcryptographyintroducingmathematicalandalgorithmicfoundations |