Computational Number Theory (discrete Mathematics And Its Applications)
by Abhijit Das /
2013 / English / PDF
2.9 MB Download
Developed from the author’s popular graduate-level course,
Developed from the author’s popular graduate-level course,Computational Number Theory
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.
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.
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.
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.
