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E-grāmata: Mathematics of Secrets: Cryptography from Caesar Ciphers to Digital Encryption

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  • Formāts: 392 pages
  • Izdošanas datums: 02-Oct-2018
  • Izdevniecība: Princeton University Press
  • Valoda: eng
  • ISBN-13: 9780691184555
  • Formāts - PDF+DRM
  • Cena: 17,02 €*
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  • Formāts: 392 pages
  • Izdošanas datums: 02-Oct-2018
  • Izdevniecība: Princeton University Press
  • Valoda: eng
  • ISBN-13: 9780691184555

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Explaining the mathematics of cryptography

The Mathematics of Secrets takes readers on a fascinating tour of the mathematics behind cryptographythe science of sending secret messages. Using a wide range of historical anecdotes and real-world examples, Joshua Holden shows how mathematical principles underpin the ways that different codes and ciphers work. He focuses on both code making and code breaking and discusses most of the ancient and modern ciphers that are currently known. He begins by looking at substitution ciphers, and then discusses how to introduce flexibility and additional notation. Holden goes on to explore polyalphabetic substitution ciphers, transposition ciphers, connections between ciphers and computer encryption, stream ciphers, public-key ciphers, and ciphers involving exponentiation. He concludes by looking at the future of ciphers and where cryptography might be headed. The Mathematics of Secrets reveals the mathematics working stealthily in the science of coded messages.

A blog describing new developments and historical discoveries in cryptography related to the material in this book is accessible at http://press.princeton.edu/titles/10826.html.

Recenzijas

"In The Mathematics of Secrets, Joshua Holden takes the reader on a chronological journey from Julius Caesars substitution cipher to modern day public-key algorithms and beyond. . . . Written for anyone with an interest in cryptography." Noel-Ann Bradshaw, Times Higher Education "Complete in surveying cryptography. . . . This is a marvelous way of illustrating the use of simple mathematics in an important application that has triggered the wit of the designers and the ingenuity of the attackers since antiquity." Adhemar Bultheel, European Mathematical Society "The best book I have seen on this subject." Phil Dyke, Leonardo Reviews "This is a fascinating tour of the mathematics behind cryptography, showing how its principles underpin the ways that different codes and ciphers operate. . . . While its all about maths, the book is accessiblebasic high school algebra is all thats needed to understand and enjoy it." Cosmos Magazine

Preface xi
Acknowledgments xiii
1 Introduction to Ciphers and Substitution
1(28)
1.1 Alice and Bob and Carl and Julius: Terminology and Caesar Cipher
1(3)
1.2 The Key to the Matter: Generalizing the Caesar Cipher
4(2)
1.3 Multiplicative Ciphers
6(9)
1.4 Affine Ciphers
15(3)
1.5 Attack at Dawn: Cryptanalysis of Sample Substitution Ciphers
18(2)
1.6 Just to Get Up That Hill: Polygraphic Substitution Ciphers
20(5)
1.7 Known-Plaintext Attacks
25(1)
1.8 Looking Forward
26(3)
2 Polyalphabetic Substitution Ciphers
29(46)
2.1 Homophonic Ciphers
29(2)
2.2 Coincidence or Conspiracy?
31(5)
2.3 Alberti Ciphers
36(3)
2.4 It's Hip to Be Square: Tabula Recta or Vigenere Square Ciphers
39(4)
2.5 How Many Is Many? Determining the Number of Alphabets
43(9)
2.6 Superman Is Staying for Dinner: Superimposition and Reduction
52(3)
2.7 Products of Polyalphabetic Ciphers
55(3)
2.8 Pinwheel Machines and Rotor Machines
58(15)
2.9 Looking Forward
73(2)
3 Transposition Ciphers
75(34)
3.1 This Is Sparta! The Scytale
75(3)
3.2 Rails and Routes: Geometric Transposition Ciphers
78(3)
3.3 Permutations and Permutation Ciphers
81(5)
3.4 Permutation Products
86(5)
3.5 Keyed Columnar Transposition Ciphers
91(6)
Sidebar 3.1 Functional Nihilism
94(3)
3.6 Determining the Width of the Rectangle
97(4)
3.7 Anagramming
101(5)
Sidebar 3.2 But When You Talk about Disruption
104(2)
3.8 Looking Forward
106(3)
4 Ciphers and Computers
109(36)
4.1 Bringing Home the Bacon: Polyliteral Ciphers and Binary Numerals
109(6)
4.2 Fractionating Ciphers
115(4)
4.3 How to Design a Digital Cipher: SP-Networks and Feistel Networks
119(11)
Sidebar 4.1 Digitizing Plaintext
125(5)
4.4 The Data Encryption Standard
130(5)
4.5 The Advanced Encryption Standard
135(8)
4.6 Looking Forward
143(2)
5 Stream Ciphers
145(37)
5.1 Running-Key Ciphers
145(8)
Sidebar 5.1 We Have All Been Here Before
150(3)
5.2 One-Time Pads
153(4)
5.3 Baby You Can Drive My Car: Autokey Ciphers
157(10)
5.4 Linear Feedback Shift Registers
167(7)
5.5 Adding Nonlinearity to LFSRs
174(4)
5.6 Looking Forward
178(4)
6 Ciphers Involving Exponentiation
182(19)
6.1 Encrypting Using Exponentiation
182(1)
6.2 Fermat's Little Theorem
183(3)
6.3 Decrypting Using Exponentiation
186(2)
6.4 The Discrete Logarithm Problem
188(2)
6.5 Composite Moduli
190(2)
6.6 The Euler Phi Function
192(3)
6.7 Decryption with Composite Moduli
195(4)
Sidebar 6.1 Fee-fi-fo-fum
197(2)
6.8 Looking Forward
199(2)
7 Public-Key Ciphers
201(40)
7.1 Right out in Public. The Idea of Public-Key Ciphers
201(6)
7.2 Diffie-Hellman Key Agreement
207(6)
7.3 Asymmetric-Key Cryptography
213(3)
7.4 RSA
216(6)
7.5 Priming the Pump: Primality Testing
222(4)
7.6 Why is RSA a (Good) Public-Key System?
226(3)
7.7 Cryptanalysis of RSA
229(4)
7.8 Looking Forward
233(2)
Appendix A The Secret History of Public-Key Cryptography
235(6)
8 Other Public-Key Systems
241(35)
8.1 The Three-Pass Protocol
241(6)
8.2 ElGamal
247(4)
8.3 Elliptic Curve Cryptography
251(14)
8.4 Digital Signatures
265(6)
8.5 Looking Forward
271(5)
9 The Future of Cryptography
276(27)
9.1 Quantum Computing
276(5)
9.2 Postquantum Cryptography
281(11)
9.3 Quantum Cryptography
292(9)
9.4 Looking Forward
301(2)
List of Symbols 303(2)
Notes 305(40)
Suggestions for Further Reading 345(4)
Bibliography 349(18)
Index 367
Joshua Holden is professor of mathematics at the Rose-Hulman Institute of Technology.