© 2018


  • 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


Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Simon Rubinstein-Salzedo
    Pages 1-3
  3. Simon Rubinstein-Salzedo
    Pages 5-8
  4. Simon Rubinstein-Salzedo
    Pages 9-23
  5. Simon Rubinstein-Salzedo
    Pages 25-39
  6. Simon Rubinstein-Salzedo
    Pages 41-54
  7. Simon Rubinstein-Salzedo
    Pages 55-62
  8. Simon Rubinstein-Salzedo
    Pages 63-73
  9. Simon Rubinstein-Salzedo
    Pages 75-83
  10. Simon Rubinstein-Salzedo
    Pages 85-87
  11. Simon Rubinstein-Salzedo
    Pages 89-98
  12. Simon Rubinstein-Salzedo
    Pages 113-126
  13. Simon Rubinstein-Salzedo
    Pages 127-140
  14. Simon Rubinstein-Salzedo
    Pages 141-155
  15. Simon Rubinstein-Salzedo
    Pages 157-171
  16. Simon Rubinstein-Salzedo
    Pages 173-189
  17. Simon Rubinstein-Salzedo
    Pages 191-205
  18. Simon Rubinstein-Salzedo
    Pages 207-219
  19. Simon Rubinstein-Salzedo
    Pages 221-230

About this book


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.



Cryptography ciphers cryptanalysis publickey cryptosystems elliptic curve cryptography RSA DiffieHellman ElGamal factorization algorithms coding theory cryptographic voting

Authors and affiliations

  1. 1.Palo AltoUSA

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.

Bibliographic information

  • Book Title Cryptography
  • Authors Simon Rubinstein-Salzedo
  • Series Title Springer Undergraduate Mathematics Series
  • Series Abbreviated Title SUMS
  • DOI
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-319-94817-1
  • eBook ISBN 978-3-319-94818-8
  • Series ISSN 1615-2085
  • Series E-ISSN 2197-4144
  • Edition Number 1
  • Number of Pages XII, 259
  • Number of Illustrations 10 b/w illustrations, 7 illustrations in colour
  • Topics Number Theory
  • Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking


“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)​