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A Course in Number Theory and Cryptography

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概要 Introduces the reader to arithmetic topics, both ancient and modern, which have been the center of interest in applica- tions of number theory, particularly in cryptography. Begins with a discussion o...f basic number theory. Algorithmic ap- proach. Inclusion of recent application of the theory of el- liptic curves. Extensive exercises.続きを見る
目次 I. Some Topics in Elementary Number Theory
{sect}1. Time estimates for doing arithmetic
{sect}2. Divisibility and the Euclidean algorithm
{sect}3. Congruences
{sect}4. Some applications to factoring
II. Finite Fields and Quadratic Residues
{sect}1. Finite fields
{sect}2. Quadratic residues and reciprocity
III. Cryptography
{sect}1. Some simple cryptosystems
{sect}2. Enciphering matrices
IV. Public Key
{sect}1. The idea of public key cryptography
{sect}2. RSA
{sect}3. Discrete log
{sect}4. Knapsack
V. Primality and Factoring
{sect}1. Pseudoprimes
{sect}2. The rho method
{sect}3. Fermat factorization and factor bases
{sect}4. The continued fraction method
VI. Elliptic Curves
{sect}1. Basic facts
{sect}2. Elliptic curve cryptosystems
{sect}3. Elliptic curve factorization
Answers to Exercises.
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登録日 2020.06.27
更新日 2020.06.28