The purpose of this book is to introduce the reader to arithmetic topics, both ancient and modern, that have been at the center of interest in applications of number theory, particularly in cryptography. No background in algebra or number theory is assumed, and the book begins with a discussion of the basic number theory that is needed. Because number theory and cryptography are fast-moving fields, this new edition contains substantial revisions and updated references.
Reihe
Auflage
Sprache
Verlagsort
Zielgruppe
Für Beruf und Forschung
Graduate
Illustrationen
Maße
Höhe: 235 mm
Breite: 155 mm
Dicke: 14 mm
Gewicht
ISBN-13
978-1-4612-6442-2 (9781461264422)
DOI
10.1007/978-1-4419-8592-7
Schweitzer Klassifikation
I. Some Topics in Elementary Number Theory.- 1. Time estimates for doing arithmetic.- 2. Divisibility and the Euclidean algorithm.- 3. Congruences.- 4. Some applications to factoring.- II. Finite Fields and Quadratic Residues.- 1. Finite fields.- 2. Quadratic residues and reciprocity.- III. Cryptography.- 1. Some simple cryptosystems.- 2. Enciphering matrices.- IV. Public Key.- 1. The idea of public key cryptography.- 2. RSA.- 3. Discrete log.- 4. Knapsack.- 5 Zero-knowledge protocols and oblivious transfer.- V. Primality and Factoring.- 1. Pseudoprimes.- 2. The rho method.- 3. Fermat factorization and factor bases.- 4. The continued fraction method.- 5. The quadratic sieve method.- VI. Elliptic Curves.- 1. Basic facts.- 2. Elliptic curve cryptosystems.- 3. Elliptic curve primality test.- 4. Elliptic curve factorization.- Answers to Exercises.
