Synopses & Reviews
This text introduces the vast and fascinating area of computational number theory. It treats algorithms for common number-theoretic problems in an elementary fashion, eliminating the need for an extensive prerequisite of algebra and analysis. The GP/PARI calculator is used throughout to demonstrate the working of arithmetic algorithms. The book contains detailed examples illustrating almost every algorithmic concept discussed. It also includes practical applications of arithmetic algorithms in public-key cryptography. Every chapter ends with many exercises and partial solutions are given in the appendix.
Synopsis
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.
With an emphasis on implementation issues, the book uses the freely available number-theory calculator GP/PARI to demonstrate complex arithmetic computations. The text includes numerous examples and exercises throughout and omits lengthy proofs, making the material accessible to students and practitioners.
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