Computational number theory Das, Abhijit

Table of Contents:

1. Arithmetic of Integers
2.Arithmetic of Finite Fields
3.Arithmetic of Polynomials
4.Arithmetic of Elliptic Curves
5. Primality Testing
6. Integer Factorization
7.Discrete Logarithms
8.Large Sparse Linear Systems
9.Public-Key Cryptography
10.Appendix A: Background
11.Appendix B: Solutions to Selected Exercises

Developed from the author’s popular graduate-level course, Computational Number Theory presents a complete treatment of number-theoretic algorithms. Avoiding advanced algebra, this self-contained text is designed for advanced undergraduate and beginning graduate students in engineering. It is also suitable for researchers new to the field and practitioners of cryptography in industry.Requiring no prior experience with number theory or sophisticated algebraic tools, the book covers many computational aspects of number theory and highlights important and interesting engineering applications. It first builds the foundation of computational number theory by covering the arithmetic of integers and polynomials at a very basic level. It then discusses elliptic curves, primality testing, algorithms for integer factorization, computing discrete logarithms, and methods for sparse linear systems. The text also shows how number-theoretic tools are used in cryptography and cryptanalysis. A dedicated chapter on the application of number theory in public-key cryptography incorporates recent developments in pairing-based cryptography.

(https://www.crcpress.com/Computational-Number-Theory/Das/9781439866153)