A Course in Number Theory and Cryptography
1st Edition
Published on 6. December 2012
VIII, 208 pages
978-1-4684-0310-7 (ISBN)
Description
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. Because number theory and cryptography are fast-moving fields, this new edition contains substantial revisions and updated references.
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Neal Koblitz
A Course in Number Theory and Cryptography
E-Book
09/2012
2nd Edition
Springer
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Neal Koblitz
A Course in Number Theory and Cryptography
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07/2012
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A Course in Number Theory and Cryptography
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08/1987
Springer
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Content
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.- V. Primality and Factoring.- §1. Pseudoprimes.- §2. The rho method.- §3. Fermat factorization and factor bases.- §4. The continued fraction method.- VI. Elliptic Curves.- §1. Basic facts.- §2. Elliptic curve cryptosystems.- §3. Elliptic curve factorization.- Answers to Exercises.
