Neal Koblitz

A Course in Number Theory and Cryptography

• Gebundenes Buch

Produktbeschreibung

The purpose of this book is to introduce the reader to arithmetic topics, both ancient and modern, which 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 which is needed. The approach taken is algorithmic, emphasizing estimates of the efficiency of the techniques which arise from the theory. A special feature is the inclusion of recent application of the theory of elliptic curves. Extensive imaginative exercises and careful, revealing answers have been included in all of the chapters. The information society and the computer age have given rise to innumerable applications for cryptography besides the original motivation of secure communication. Thus, cryptography is a relatively fast-moving field. The new edition contains due to that fact substantial revisions and updated references.

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Produktdetails

• Graduate Texts in Mathematics
• Verlag: Springer, Berlin
• 2nd ed.
• Seitenzahl: 248
• Erscheinungstermin: 2. September 1994
• Englisch
• Abmessung: 241mm x 160mm x 19mm
• Gewicht: 524g
• ISBN-13: 9783540942931
• ISBN-10: 3540942939
• Artikelnr.: 05584997

Inhaltsangabe

1: Some Topics in Elementary Number Theory.

2: Finite Fields and Quadratic Residues.

3: Cryptography.

4: Public Key.

5: Primality and Factoring.

6: Elliptic Curves.

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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.