Modern cryptography and elliptic curves : a beginner's guide
 Responsibility
 Thomas R. Shemanske.
 Publication
 Providence, Rhode Island : American Mathematical Society, [2017]
 Physical description
 xii, 250 pages : illustrations ; 22 cm.
 Series
 Student mathematical library ; v. 83.
Access
Available online
Science Library (Li and Ma)
Stacks
Call number  Status 

QA567.2 .E44 S534 2017  Unknown 
More options
Creators/Contributors
 Author/Creator
 Shemanske, Thomas R., 1952
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 * Three motivating problems* Back to the beginning* Some elementary number theory* A second view of modular arithmetic: $\mathbb{Z}_n$ and $U_n$* Publickey cryptography and RSA* A little more algebra* Curves in affine and projective space* Applications of elliptic curves* Deeper results and concluding thoughts* Answers to selected exercises* Bibliography* Index.
 (source: Nielsen Book Data)9781470435820 20170814
 Publisher's Summary
 This book offers the beginning undergraduate student some of the vista of modern mathematics by developing and presenting the tools needed to gain an understanding of the arithmetic of elliptic curves over finite fields and their applications to modern cryptography. This gradual introduction also makes a significant effort to teach students how to produce or discover a proof by presenting mathematics as an exploration, and at the same time, it provides the necessary mathematical underpinnings to investigate the practical and implementation side of elliptic curve cryptography (ECC). Elements of abstract algebra, number theory, and affine and projective geometry are introduced and developed, and their interplay is exploited. Algebra and geometry combine to characterize congruent numbers via rational points on the unit circle, and group law for the set of points on an elliptic curve arises from geometric intuition provided by Bezout's theorem as well as the construction of projective space. The structure of the unit group of the integers modulo a prime explains RSA encryption, Pollard's method of factorization, DiffieHellman key exchange, and ElGamal encryption, while the group of points of an elliptic curve over a finite field motivates Lenstra's elliptic curve factorization method and ECC. The only real prerequisite for this book is a course on onevariable calculus; other necessary mathematical topics are introduced onthefly. Numerous exercises further guide the exploration.
(source: Nielsen Book Data)9781470435820 20170814
Subjects
 Subject
 Curves, Elliptic > Textbooks.
 Geometry, Algebraic > Textbooks.
 Cryptography > Textbooks.
 Cryptography.
 Curves, Elliptic.
 Geometry, Algebraic.
 Number theory > Instructional exposition (textbooks, tutorial papers, etc.)
 Computer science > Instructional exposition (textbooks, tutorial papers, etc.)
 Number theory > Elementary number theory > Elementary number theory.
 Algebraic geometry > Arithmetic problems. Diophantine geometry > Applications to coding theory and cryptography.
 Number theory > Finite fields and commutative rings (numbertheoretic aspects) > Algebraic coding theory; cryptography.
 Computer science > Theory of data > Data encryption.
 Number theory > Computational number theory > Factorization.
 Information and communication, circuits > Communication, information > Cryptography.
 Number theory > Arithmetic algebraic geometry (Diophantine geometry) > Elliptic curves over global fields.
 Quantum theory > Axiomatics, foundations, philosophy > Quantum computation.
 Genre
 Textbooks.
Bibliographic information
 Publication date
 2017
 Series
 Student mathematical library ; volume 83
 ISBN
 9781470435820 (alk. paper)
 1470435829 (alk. paper)