- 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
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- About this Textbook
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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. - About the authors
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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.
- Reviews
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“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 a copy of this book within easy reach.” (Mark Hunacek, MAA Reviews, January, 2019)
- Table of contents (20 chapters)
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A Quick Overview
Pages 1-3
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Cæsar Ciphers
Pages 5-8
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Substitution Ciphers
Pages 9-23
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A First Look at Number Theory
Pages 25-39
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The Vigenère Cipher
Pages 41-54
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Table of contents (20 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Cryptography
- Authors
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- Simon Rubinstein-Salzedo
- Series Title
- Springer Undergraduate Mathematics Series
- Copyright
- 2018
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer Nature Switzerland AG
- eBook ISBN
- 978-3-319-94818-8
- DOI
- 10.1007/978-3-319-94818-8
- Softcover ISBN
- 978-3-319-94817-1
- Series ISSN
- 1615-2085
- Edition Number
- 1
- Number of Pages
- XII, 259
- Number of Illustrations
- 10 b/w illustrations, 7 illustrations in colour
- Topics
*immediately available upon purchase as print book shipments may be delayed due to the COVID-19 crisis. ebook access is temporary and does not include ownership of the ebook. Only valid for books with an ebook version. Springer Reference Works and instructor copies are not included.
