Cryptography
Springer International Publishing (Verlag)
978-3-319-94817-1 (ISBN)
Beginning with classical ciphers and their cryptanalysis, this book proceeds to focus on modern public key cryptosystems such as Diffie-Hellman, ElGamal, RSA, and elliptic curve cryptography with an analysis of vulnerabilities of these systems and underlying mathematical issues such as factorization algorithms. Specialized topics such as zero knowledge proofs, cryptographic voting, coding theory, and new research are covered in the final section of this book.
Aimed at undergraduate students, this book contains a large selection of problems, ranging from straightforward to difficult, and can be used as a textbook for classes as well as self-study. Requiring only a solid grounding in basic mathematics, this book will also appeal to advanced high school students and amateur mathematicians interested in this fascinating and topical subject.
Simon Rubinstein-Salzedo received his PhD in mathematics from Stanford University in 2012. Afterwards, he taught at Dartmouth College and Stanford University. In 2015, he founded Euler Circle, a mathematics institute in the San Francisco Bay Area, dedicated to teaching college-level mathematics classes to advanced high-school students, as well as mentoring them on mathematics research. His research interests include number theory, algebraic geometry, combinatorics, probability, and game theory.
Introduction. -1. A quick overview. -2. Caesar ciphers. -3. Substitution ciphers. -4. A first look at number theory. -5. The Vigenère cipher. -6. The Hill Cipher. -7. Other types of ciphers. -8. Big O notion and algorithm efficiency. -9. Abstract Algebra. -10. A second look at number theory. -11. The Diffie-Hellman Cryptosystem and the Discrete Logarithm Problem. -12. The RSA Cryptosystem. -13. Clever factorization algorithms and primality testing. -14. Elliptic curves. -15. The versatility of elliptic curves. -16. Zero-Knowledge Proofs. -17. Secret sharing, visual cryptography, and voting. -18. Quantum Computing and Quantum Cryptography. -19. Markov chains. -20. Some coding theory. -Bibliography. -Index.
"The present book presents a good undergraduate introduction to cryptography from its earliest roots to contemporary cryptosystems. It also contains all the necessary mathematical background for its comprehension and a large selection of problems." (Dimitros Poulakis, zbMATH 1408.94001, 2019)
"There is certainly a lot of interesting mathematics to be learned here, and the reader will have fun learning it. If I were teaching a course in cryptography, this text would definitely be on my very short list; people teaching a course in number theory who want to discuss some cryptography might also want to keep acopy of this book within easy reach." (Mark Hunacek, MAA Reviews, January, 2019)“The present book presents a good undergraduate introduction to cryptography from its earliest roots to contemporary cryptosystems. It also contains all the necessary mathematical background for its comprehension and a large selection of problems.” (Dimitros Poulakis, zbMATH 1408.94001, 2019)“There is certainly a lot of interesting mathematics to be learned here, and the reader will have fun learning it. If I were teaching a course in cryptography, this text would definitely be on my very short list; people teaching a course in number theory who want to discuss some cryptography might also want to keep acopy of this book within easy reach.” (Mark Hunacek, MAA Reviews, January, 2019)
| Erscheinungsdatum | 19.10.2018 |
|---|---|
| Reihe/Serie | Springer Undergraduate Mathematics Series |
| Zusatzinfo | XII, 259 p. 17 illus., 7 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 421 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
| Mathematik / Informatik ► Mathematik ► Graphentheorie | |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| Schlagworte | ciphers • coding theory • combinatorics • Cryptanalysis • cryptographic voting • cryptography • DiffieHellman • ElGamal • Elliptic Curve Cryptography • factorization algorithms • publickey cryptosystems • rsa |
| ISBN-10 | 3-319-94817-2 / 3319948172 |
| ISBN-13 | 978-3-319-94817-1 / 9783319948171 |
| Zustand | Neuware |
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