Elementary number theory, cryptography and codes
 Responsibility
 Maria Welleda Baldoni, Ciro Ciliberto, Giulia Maria Piacentini Cattaneo.
 Uniform Title
 Aritmetica, crittografia, e codici. English
 Language
 English.
 Imprint
 Berlin : Springer, c2009.
 Physical description
 xvi, 522 p. : ill. ; 24 cm.
 Series
 Universitext.
Access
Available online
 dx.doi.org SpringerLink
Math & Statistics Library

Stacks

Unknown
QA37.3 .B35 2009

Unknown
QA37.3 .B35 2009
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Creators/Contributors
 Author/Creator
 Baldoni, M. Welleda, 1949
 Contributor
 Ciliberto, C. (Ciro), 1950
 Piacentini Cattaneo, Giulia Maria.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. [507]509) and index.
 Contents

 1 A roundup on numbers. 2 Computational complexity. 3 From the infinite to the finite. 4 Finite is not enough: factorising integers. 5 Finite fields and polynomial congruences. 6 Primality and factorisation tests. 7 Secrets... and lies. 8 Transmitting without... fear of errors. 9 The future is already here: quantum cryptography. 10 Solution to selected exercises. References. Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 In this volume one finds basic techniques from algebra and number theory (e.g. congruences, unique factorization domains, finite fields, quadratic residues, primality tests, continued fractions, etc.) which in recent years have proven to be extremely useful for applications to cryptography and coding theory. Both cryptography and codes have crucial applications in our daily lives, and they are described here, while the complexity problems that arise in implementing the related numerical algorithms are also taken into due account. Cryptography has been developed in great detail, both in its classical and more recent aspects. In particular public key cryptography is extensively discussed, the use of algebraic geometry, specifically of elliptic curves over finite fields, is illustrated, and a final chapter is devoted to quantum cryptography, which is the new frontier of the field. Coding theory is not discussed in full; however a chapter, sufficient for a good introduction to the subject, has been devoted to linear codes. Each chapter ends with several complements and with an extensive list of exercises, the solutions to most of which are included in the last chapter. Though the book contains advanced material, such as cryptography on elliptic curves, Goppa codes using algebraic curves over finite fields, and the recent AKS polynomial primality test, the authors' objective has been to keep the exposition as selfcontained and elementary as possible. Therefore the book will be useful to students and researchers, both in theoretical (e.g. mathematicians) and in applied sciences (e.g. physicists, engineers, computer scientists, etc.) seeking a friendly introduction to the important subjects treated here. The book will also be useful for teachers who intend to give courses on these topics.
(source: Nielsen Book Data)  Supplemental links
 Table of contents:
Subjects
Bibliographic information
 Publication date
 2009
 Series
 Universitext
 Note
 Originally published in Italian as: Aritmetica, crittografia e codici. Milano : Springer, 2006.
 ISBN
 9783540691990
 3540691995
 9783540692003 (electronic)
 3540692002 (electronic)
 Publisher Number
 12263400