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QUANTUM COMPUTATIONAL NUMBER THEORY IBD

SONG Y YAN
SPRINGER
03 / 2018
9783319798462
Inglés

Sinopsis

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.áThe author discusses quantum algorithms for solving the Integer Factorization Problem (IFP), the Discrete Logarithm Problem (DLP), and the Elliptic Curve Discrete Logarithm Problemá(ECDLP) and for attacking IFP, DLP and ECDLP based cryptographic systems. Chapters also cover various other quantum algorithms for PellâÇÖs equation, principal ideal, unit group, class group, Gauss sums, prime counting function, RiemannâÇÖs hypothesis and the BSD conjecture.Quantum Computational Number Theoryáis self-contained and intended to be used either as a graduate text in computing, communications and mathematics, or as a basic reference in the related fields.áNumber theorists, cryptographers and professionals working in quantum computing, cryptography and network security will find this book a valuable asset.