A Computational Number Theory & Algebra by Victor Shoup
A Computational Number Theory & Algebra - 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 Zp
- 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
What You Will Learn in A Computational Number Theory & Algebra
A Computational Introduction to Number Theory and Algebra by Victor Shoup bridges fundamental abstract algebra with concrete algorithmic analysis. Downloading this victor shoup computational number theory pdf gives students, researchers, and computer scientists structured exposure to efficient mathematical computing.
The textbook covers modular arithmetic, prime testing, polynomial factorization, finite fields, abelian groups, and public-key cryptography algorithms. Studying this complete victor shoup number theory algebra book equips computer science and mathematics majors with essential tools for cryptographic protocol design and algorithmic analysis.
Designed as an essential shoup computational number theory pdf reference, this text features rigorous mathematical proofs, algorithmic complexity estimates, and comprehensive exercise sets.
Book Details & Specifications
Title:
A Computational Number Theory & Algebra by Victor Shoup
Publisher:
Cambridge University Press
Year:
2010
Pages:
743
Type:
PDF
Language:
English
ISBN-10 #:
0521516447
ISBN-13 #:
978-0521516440
License:
CC BY-NC-ND 3.0
Amazon:
Amazon
About the Author: Victor Shoup
The author Victor Shoup
is a Professor of Computer Science at New York University (NYU) and a distinguished researcher in cryptography and computational number theory.
As the author of A Computational Introduction to Number Theory and Algebra by Victor Shoup and creator of NTL (Number Theory Library), his work has profoundly shaped modern cryptographic software standards and complexity analysis.
Read or Downloadable A Computational Number Theory & Algebra
Free Number Theory Books PDF | Curated Academic Library Index