商品描述
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.
商品描述(中文翻譯)
這本書提供了計算數論和算法方面的進階主題的全面介紹，重點在於其在密碼學中的應用。讀者將學習開發快速算法，包括量子算法，以解決各種經典和現代的數論問題。主要問題包括質數生成、質數測試、整數因式分解、離散對數、橢圓曲線運算、猜想和數值驗證。
作者討論了解決整數因式分解問題（Integer Factorization Problem, IFP）、離散對數問題（Discrete Logarithm Problem, DLP）和橢圓曲線離散對數問題（Elliptic Curve Discrete Logarithm Problem, ECDLP）的量子算法，以及攻擊基於IFP、DLP和ECDLP的密碼系統的算法。各章節還涵蓋了其他各種量子算法，針對佩爾方程（Pell's equation）、主理想（principal ideal）、單位群（unit group）、類群（class group）、高斯和（Gauss sums）、質數計數函數（prime counting function）、黎曼假設（Riemann's hypothesis）和BSD猜想（BSD conjecture）。
《量子計算數論》（Quantum Computational Number Theory）是自成一體的，旨在用作計算、通信和數學的研究生教材，或作為相關領域的基本參考資料。數論學家、密碼學家以及從事量子計算、密碼學和網絡安全的專業人士將會發現這本書是一個寶貴的資產。
