Computational Number Theory (Discrete Mathematics and Its by Abhijit Das PDF

By Abhijit Das

Developed from the author’s well known graduate-level path, Computational quantity Theory offers an entire therapy of number-theoretic algorithms. heading off complicated algebra, this self-contained textual content is designed for complex undergraduate and starting graduate scholars in engineering. it's also compatible for researchers new to the sphere and practitioners of cryptography in industry.

Requiring no previous adventure with quantity thought or refined algebraic instruments, the publication covers many computational points of quantity conception and highlights vital and engaging engineering purposes. It first builds the basis of computational quantity concept by means of overlaying the mathematics of integers and polynomials at a really simple point. It then discusses elliptic curves, primality checking out, algorithms for integer factorization, computing discrete logarithms, and strategies for sparse linear structures. The textual content additionally exhibits how number-theoretic instruments are utilized in cryptography and cryptanalysis. A devoted bankruptcy at the software of quantity conception in public-key cryptography accommodates fresh advancements in pairing-based cryptography.

With an emphasis on implementation matters, the ebook makes use of the freely to be had number-theory calculator GP/PARI to illustrate complicated mathematics computations. The textual content comprises a variety of examples and routines all through and omits long proofs, making the cloth obtainable to scholars and practitioners.

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