Springer Undergraduate Mathematics Series

Cryptography

Authors: Rubinstein-Salzedo, Simon

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  • 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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  • ISBN 978-3-319-94818-8
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  • ISBN 978-3-319-94817-1
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About this Textbook

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

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

“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)

Table of contents (20 chapters)
  • A Quick Overview

    Pages 1-3

    Rubinstein-Salzedo, Simon

  • Cæsar Ciphers

    Pages 5-8

    Rubinstein-Salzedo, Simon

  • Substitution Ciphers

    Pages 9-23

    Rubinstein-Salzedo, Simon

  • A First Look at Number Theory

    Pages 25-39

    Rubinstein-Salzedo, Simon

  • The Vigenère Cipher

    Pages 41-54

    Rubinstein-Salzedo, Simon

Buy this book

eBook n/a
  • ISBN 978-3-319-94818-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
Softcover n/a
  • ISBN 978-3-319-94817-1
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Cryptography
Authors
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