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Computational Introduction to Number Theory Book Free Download

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A Computational Introduction to Number Theory
and Algebra
(Version 2)
Victor Shoup

Table of Contents

1 Basic properties of the integers

2 Congruences

3 Computing with large integers

4 Euclid’s algorithm

5 The distribution of primes

6 Abelian groups

7 Rings

8 Finite and discrete probability distributions

9 Probabilistic algorithms

10 Probabilistic primality testing

11 Finding generators and discrete logarithms in Z∗

12 Quadratic reciprocity and computing modular square roots

13 Modules and vector spaces

14 Matrices

15 Subexponential-time discrete logarithms and factoring

16 More rings

17 Polynomial arithmetic and applications

18 Linearly generated sequences and applications

19 Finite fields

20 Algorithms for finite fields

21 Deterministic primality testing

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