ENGLISH

Quantum Computational Number Theory

By Song Y. Yan

Book information

Publisher
Springer
Year
2015
ISBN
3319258214, 9783319258218
DOI
10.1007/978-3-319-25823-2
Language
english
Format
PDF
Filesize
3 MB (2931433 bytes)
Pages
259\259
Time added
2016-01-11 20:30:03
Theory of Computation; Systems and Data Security;

Description

This book provides a comprehensive introduction to advanced topics in the computational and algorithmic aspects of number theory, focusing on applications in cryptography. Readers will learn to develop fast algorithms, including quantum algorithms, to solve various classic and modern number theoretic problems. Key problems include prime number generation, primality testing, integer factorization, discrete logarithms, elliptic curve arithmetic, conjecture and numerical verification. The author discusses quantum algorithms for solving the Integer Factorization Problem (IFP), the Discrete Logarithm Problem (DLP), and the Elliptic Curve Discrete Logarithm Problem (ECDLP) and for attacking IFP, DLP and ECDLP based cryptographic systems. Chapters also cover various other quantum algorithms for Pells equation, principal ideal, unit group, class group, Gauss sums, prime counting function, Riemanns hypothesis and the BSD conjecture.

Similar books