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© LIBERO v6.4.1sp220816
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Catalogue Tag Display
MARC 21
Elementary Number Theory, Cryptography and Codes
Tag
Description
020
$a9783540692003
082
$a511.6
099
$aOnline Resource: Springer
100
$aBaldoni, Maria Welleda$d1949-
245
$aElementary Number Theory, Cryptography and Codes$h[Ebook]$cby Maria Welleda Baldoni, Ciro Ciliberto, Giulia Maria Piacentini Cattaneo
260
$aBerlin, Heidelberg$bSpringer Berlin Heidelberg$c2009
300
$axvi, 522 pages$bonline resource.
336
$atext
338
$aonline resource
440
$aUniversitext
505
$a
1 A round-up 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.
520
$a
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 self-contained 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.
538
$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
700
$aCiliberto, Ciro.$eauthor.
700
$aPiacentini Cattaneo, Giulia Maria.$eauthor.
710
$aSpringerLink (Online service)
830
$aUniversitext
856
$u
http://dx.doi.org/10.1007/978-3-540-69200-3
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