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Beschreibung
This text introduces cryptography, from its earliest roots to cryptosystems used today for secure online communication.
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.
This text introduces cryptography, from its earliest roots to cryptosystems used today for secure online communication.
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.
Über den Autor
Clark Bray is an Associate Professor of the Practice in the Department of Mathematics at Duke University. He graduated from Rice University in 1993, cum laude, with majors in Mathematics and Physics, and finished his Ph.D. in Mathematics at Stanford University in 1999, studying algebraic topology with Professor Gunnar Carlsson. While subsequently a Lecturer at Stanford, he created and taught a program in algebraic topology for talented high school math students at the Stanford University Mathematics Camp (SUMaC) in 2001-2003.
Adrian Butscher received his [...]. in mathematics and physics at the University of Toronto and his Ph.D. in mathematics at Stanford University. After a fifteen-year period in academia, conducting research in pure and applied differential geometry and teaching at all levels of the undergraduate and graduate curricula, Adrian now works as a research scientist with Autodesk, Inc., a global software company that creates digital design tools for the manufacturing, architecture, building, construction, media, and entertainment industries. While at Stanford, Adrian served as a counsellor and instructor for SuMAC, the Stanford University Mathematics Camp, a month-long, immersive educational experience for mathematically gifted high school students.
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.
Zusammenfassung
Outlines cryptography from its earliest roots to its modern use in daily transactions
Contains numerous problems to practice techniques
Examines classical ciphers, modern public key cryptosystems, and specialized topics
Inhaltsverzeichnis
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.
Details
| Erscheinungsjahr: | 2018 |
|---|---|
| Fachbereich: | Wahrscheinlichkeitstheorie |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Reihe: | Springer Undergraduate Mathematics Series |
| Inhalt: |
xii
259 S. 10 s/w Illustr. 7 farbige Illustr. 259 p. 17 illus. 7 illus. in color. |
| ISBN-13: | 9783319948171 |
| ISBN-10: | 3319948172 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-319-94817-1 |
| Einband: | Kartoniert / Broschiert |
| Autor: | Rubinstein-Salzedo, Simon |
| Hersteller: |
Springer
Springer International Publishing AG Springer Undergraduate Mathematics Series |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 235 x 155 x 14 mm |
| Von/Mit: | Simon Rubinstein-Salzedo |
| Erscheinungsdatum: | 17.10.2018 |
| Gewicht: | 0,467 kg |
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