Quantum Computational Number Theory
Springer International Publishing (Verlag)
978-3-319-25821-8 (ISBN)
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.
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.
"Over the last two decades, the field of quantum computational number theory (QCNT) has grown, and this book summarizes the major developments in the area. ... I strongly recommend the book to all young computer science students and to mathematicians who love number theory so they can enjoy this new field." (Manish Gupta, Computing Reviews, April, 2017)
| Erscheinungsdatum | 28.12.2015 |
|---|---|
| Zusatzinfo | IX, 252 p. 40 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
| Schlagworte | Coding and information theory • computational complexity theory • Computational Number Theory • Computer Algorithms • Computer Science • cryptography • data encryption • design and analysis of algorithms • Digital Signatures • discrete logarithm • Elliptic curve arithmetic • Fast computation • Integer Factorization • number-theoretic algorithms • Public-Key Cryptography • Quantum computational number theory • Quantum Computing • systems and data security • Theory of Computation |
| ISBN-10 | 3-319-25821-4 / 3319258214 |
| ISBN-13 | 978-3-319-25821-8 / 9783319258218 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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