Softcover ISBN:  9780821883211 
Product Code:  MAWRLD/29 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
eBook ISBN:  9781470415945 
Product Code:  MAWRLD/29.E 
List Price:  $55.00 
MAA Member Price:  $49.50 
AMS Member Price:  $44.00 
Softcover ISBN:  9780821883211 
eBook: ISBN:  9781470415945 
Product Code:  MAWRLD/29.B 
List Price:  $120.00 $92.50 
MAA Member Price:  $108.00 $83.25 
AMS Member Price:  $96.00 $74.00 
Softcover ISBN:  9780821883211 
Product Code:  MAWRLD/29 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
eBook ISBN:  9781470415945 
Product Code:  MAWRLD/29.E 
List Price:  $55.00 
MAA Member Price:  $49.50 
AMS Member Price:  $44.00 
Softcover ISBN:  9780821883211 
eBook ISBN:  9781470415945 
Product Code:  MAWRLD/29.B 
List Price:  $120.00 $92.50 
MAA Member Price:  $108.00 $83.25 
AMS Member Price:  $96.00 $74.00 

Book DetailsMathematical WorldVolume: 29; 2013; 332 ppMSC: Primary 94; 68; 01
How quickly can you compute the remainder when dividing \(109837^{97}\) by 120143? Why would you even want to compute this? And what does this have to do with cryptography?
Modern cryptography lies at the intersection of mathematics and computer sciences, involving number theory, algebra, computational complexity, fast algorithms, and even quantum mechanics. Many people think of codes in terms of spies, but in the information age, highly mathematical codes are used every day by almost everyone, whether at the bank ATM, at the grocery checkout, or at the keyboard when you access your email or purchase products online.
This book provides a historical and mathematical tour of cryptography, from classical ciphers to quantum cryptography. The authors introduce just enough mathematics to explore modern encryption methods, with nothing more than basic algebra and some elementary number theory being necessary. Complete expositions are given of the classical ciphers and the attacks on them, along with a detailed description of the famous Enigma system. The publickey system RSA is described, including a complete mathematical proof that it works. Numerous related topics are covered, such as efficiencies of algorithms, detecting and correcting errors, primality testing and digital signatures. The topics and exposition are carefully chosen to highlight mathematical thinking and problem solving. Each chapter ends with a collection of problems, ranging from straightforward applications to more challenging problems that introduce advanced topics. Unlike many books in the field, this book is aimed at a general liberal arts student, but without losing mathematical completeness.
A complete solution key is available for instructors upon request. Send email to Steven.J.Miller@williams.edu or Steven.Miller.MC.96@ya.yale.edu.
ReadershipUndergraduate students interested in cryptography and elementary number theory.

Table of Contents

Chapters

1. Historical introduction

2. Classical cryptology: Methods

3. Enigma and Ultra

4. Classical cryptography: Attacks I

5. Classical cryptography: Attacks II

6. Modern symmetric encryption

7. Introduction to publicchannel cryptography

8. Publicchannel cryptography

9. Error detecting and correcting codes

10. Modern cryptography

11. Primality testing and factorization

12. Solutions to selected exercises


Additional Material

Reviews

The authors have done an excellent job of presenting this material in as painless and accessible way as possible.
MAA Reviews


RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a coursePermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Reviews
 Requests
How quickly can you compute the remainder when dividing \(109837^{97}\) by 120143? Why would you even want to compute this? And what does this have to do with cryptography?
Modern cryptography lies at the intersection of mathematics and computer sciences, involving number theory, algebra, computational complexity, fast algorithms, and even quantum mechanics. Many people think of codes in terms of spies, but in the information age, highly mathematical codes are used every day by almost everyone, whether at the bank ATM, at the grocery checkout, or at the keyboard when you access your email or purchase products online.
This book provides a historical and mathematical tour of cryptography, from classical ciphers to quantum cryptography. The authors introduce just enough mathematics to explore modern encryption methods, with nothing more than basic algebra and some elementary number theory being necessary. Complete expositions are given of the classical ciphers and the attacks on them, along with a detailed description of the famous Enigma system. The publickey system RSA is described, including a complete mathematical proof that it works. Numerous related topics are covered, such as efficiencies of algorithms, detecting and correcting errors, primality testing and digital signatures. The topics and exposition are carefully chosen to highlight mathematical thinking and problem solving. Each chapter ends with a collection of problems, ranging from straightforward applications to more challenging problems that introduce advanced topics. Unlike many books in the field, this book is aimed at a general liberal arts student, but without losing mathematical completeness.
A complete solution key is available for instructors upon request. Send email to Steven.J.Miller@williams.edu or Steven.Miller.MC.96@ya.yale.edu.
Undergraduate students interested in cryptography and elementary number theory.

Chapters

1. Historical introduction

2. Classical cryptology: Methods

3. Enigma and Ultra

4. Classical cryptography: Attacks I

5. Classical cryptography: Attacks II

6. Modern symmetric encryption

7. Introduction to publicchannel cryptography

8. Publicchannel cryptography

9. Error detecting and correcting codes

10. Modern cryptography

11. Primality testing and factorization

12. Solutions to selected exercises

The authors have done an excellent job of presenting this material in as painless and accessible way as possible.
MAA Reviews