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books.google.com - How quickly can you compute the remainder when dividing 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...https://books.google.com/books/about/The_Mathematics_of_Encryption_An_Element.html?id=GbKyAAAAQBAJ&utm_source=gb-gplus-shareThe Mathematics of Encryption: An Elementary Introduction Buy eBook - $38.71Get this book in print

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# The Mathematics of Encryption: An Elementary Introduction

Margaret Cozzens, Steven J. Miller American Mathematical Soc., Sep 5, 2013 - Mathematics - 332 pages 0 Reviewshttps://books.google.com/books/about/The_Mathematics_of_Encryption_An_Element.html?id=GbKyAAAAQBAJHow quickly can you compute the remainder when dividing img style="width: 8px; height: 12px; margin-right: 0.069em;" src="http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0031.png"img style="width: 8px; height: 12px; margin-right: 0.038em;" src="http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0030.png"img style="width: 8px; height: 12px; margin-right: 0.042em;" src="http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0039.png"img style="width: 8px; height: 12px; margin-right: 0.041em;" src="http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0038.png"img style="width: 8px; height: 12px; margin-right: 0.041em;" src="http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0033.png"img style="width: 9px; height: 12px; margin-right: 0.014em;" src="http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0037.png" img style="width: 6px; height: 8px; margin-right: 0.041em;" src="http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Main/Regular/085/0039.png"img style="width: 6px; height: 8px; margin-right: 0.014em;" src="http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Main/Regular/085/0037.png" 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 public-key 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.

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Page 2

Title Page

Table of Contents

Index

References

### Contents

Methods 19 Enigma and Ultra 51 Attacks I 81 Attacks II 113 Modern Symmetric Encryption 133 Introduction to PublicChannel Cryptography 171 PublicChannel Cryptography 213 Error Detecting and Correcting Codes 239 Modern Cryptography 269 Primality Testing and Factorization 289 Solutions to Selected Problems 317 Bibliography 325 Copyright### Common terms and phrases

affine cipher Alice BabyBlock BabyCSS binary number bits blocks break brute force Caesar cipher Carmichael numbers Chapter check digits choose ciphertext codewords color compute congruences correct corresponds cryptography decode decryption discuss encode encrypt the message encrypted message encryption schemes encryption stream Enigma example Exercise extended Euclidean algorithm factor Fermat’s little Theorem Figure frequency analysis Germans gives graph greatest common divisor guess hash function hash value Hill cipher inverse keystream keyword KidRSA known-plaintext attack large numbers length LFSR LFSRsum look mathematics matrix means method modulo 26 multiple number of possible odd number one-time pad output pair perfect code permutation cipher photon pixel plaintext positive integer primality test prime numbers problem proof random relatively prime rotors secret sequence shift solve steganography string substitution alphabet ciphers subtract there’s transmit vertices Vigen`ere cipher words### About the author (2013)

Margaret Cozzens, DIMACS, Rutgers University, Piscataway, NJ, USASteven J. Miller, Williams College, Williamstown, MA, USA

### Bibliographic information

Title The Mathematics of Encryption: An Elementary Introduction*Volume 29 of Mathematical World*Authors Margaret Cozzens, Steven J. Miller Edition illustrated Publisher American Mathematical Soc., 2013 ISBN 0821883216, 9780821883211 Length 332 pages Subjects Mathematics › General

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