 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

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 DiffieHellman, 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 selfstudy. 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 RubinsteinSalzedo 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 collegelevel mathematics classes to advanced highschool 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)


A Quick Overview
Pages 13

Cæsar Ciphers
Pages 58

Substitution Ciphers
Pages 923

A First Look at Number Theory
Pages 2539

The Vigenère Cipher
Pages 4154

Table of contents (20 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Cryptography
 Authors

 Simon RubinsteinSalzedo
 Series Title
 Springer Undergraduate Mathematics Series
 Copyright
 2018
 Publisher
 Springer International Publishing
 Copyright Holder
 Springer Nature Switzerland AG
 eBook ISBN
 9783319948188
 DOI
 10.1007/9783319948188
 Softcover ISBN
 9783319948171
 Series ISSN
 16152085
 Edition Number
 1
 Number of Pages
 XII, 259
 Number of Illustrations
 10 b/w illustrations, 7 illustrations in colour
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