Quantum Computational Number Theory

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 theoreti...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Yan, Song Y. (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Springer, 2015.
Edición:1st ed. 2015.
Temas:
Computer science.
Data protection.
Coding theory.
Information theory.
Cryptography.
Data encryption (Computer science).
Theory of Computation.
Data and Information Security.
Coding and Information Theory.
Cryptology.
Acceso en línea:Texto Completo

MARC

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245 1 0 |a Quantum Computational Number Theory  |h [electronic resource] /  |c by Song Y. Yan. 
250 |a 1st ed. 2015. 
264 1 |a Cham :  |b Springer International Publishing :  |b Imprint: Springer,  |c 2015. 
300 |a IX, 252 p. 40 illus. in color.  |b online resource. 
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505 0 |a Introduction -- Classical and Quantum Computation -- Quantum Computing for Integer Factorization -- Quantum Computing for Discrete Logarithms -- Quantum Computing for Elliptic Curve Discrete Logarithms -- Miscellaneous Quantum Algorithms. 
520 |a 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 Pell's equation, principal ideal, unit group, class group, Gauss sums, prime counting function, Riemann's hypothesis and the BSD conjecture. Quantum Computational Number Theory is 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. Number theorists, cryptographers and professionals working in quantum computing, cryptography and network security will find this book a valuable asset. 
650 0 |a Computer science. 
650 0 |a Data protection. 
650 0 |a Coding theory. 
650 0 |a Information theory. 
650 0 |a Cryptography. 
650 0 |a Data encryption (Computer science). 
650 1 4 |a Theory of Computation. 
650 2 4 |a Data and Information Security. 
650 2 4 |a Coding and Information Theory. 
650 2 4 |a Cryptology. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer Nature eBook 
776 0 8 |i Printed edition:  |z 9783319258218 
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950 |a Computer Science (SpringerNature-11645) 
950 |a Computer Science (R0) (SpringerNature-43710) 

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