Quantum Computational Number Theory
Song Y. Yan
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.
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.
Tahun:
2015
Penerbit:
Springer
Bahasa:
english
Halaman:
259
ISBN 10:
3319258214
ISBN 13:
9783319258218
File:
PDF, 2.80 MB
IPFS:
,
english, 2015
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