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Modern Cryptography Volume 1
This open access book systematically explores the statistical characteristics of cryptographic systems, the computational complexity theory of cryptographic algorithms and the mathematical principles behind various encryption and decryption algorithms. The theory stems from technology. Based on Shannon's information theory, this book systematically introduces the information theory, statistical characteristics and computational complexity theory of public key cryptography, focusing on the three main algorithms of public key cryptography, RSA, discrete logarithm and elliptic curve cryptosystem. It aims to indicate what it is and why it is. It systematically simplifies and combs the theory and technology of lattice cryptography, which is the greatest feature of this book. It requires a good knowledge in algebra, number theory and probability statistics for readers to read this book. The senior students majoring in mathematics, compulsory for cryptography and science and engineering postgraduates will find this book helpful. It can also be used as the main reference book for researchers in cryptography and cryptographic engineering areas. [Resumen de la editorial]
Modern Cryptography Volume 2
This open access book covers the most cutting-edge and hot research topics and fields of post-quantum cryptography. The main purpose of this book is to focus on the computational complexity theory of lattice ciphers, especially the reduction principle of Ajtai, in order to fill the gap that post-quantum ciphers focus on the implementation of encryption and decryption algorithms, but the theoretical proof is insufficient. In Chapter 3, Chapter 4 and Chapter 6, author introduces the theory and technology of LWE distribution, LWE cipher and homomorphic encryption in detail. When using random analysis tools, there is a problem of "ambiguity" in both definition and algorithm. The greatest feature...
Proceedings of the First International Forum on Financial Mathematics and Financial Technology
This book contains high-quality papers presented at the First International Forum on Financial Mathematics and Financial Technology. With the rapid development of FinTech, the in-depth integration between mathematics, finance and advanced technology is the general trend. This book focuses on selected aspects of the current and upcoming trends in FinTech. In detail, the included scientific papers focus on financial mathematics and FinTech, presenting the innovative mathematical models and state-of-the-art technologies such as deep learning, with the aim to improve our financial analysis and decision-making and enhance the quality of financial services and risk control. The variety of the papers delivers added value for both scholars and practitioners where they will find perfect integration of elegant mathematical models and up-to-date data mining technologies in financial market analysis.
Proceedings of the Second International Forum on Financial Mathematics and Financial Technology
This open access book is the documentary of the Second International Forum on Financial Mathematics and Financial Technology, with focus on selected aspects of the current and upcoming trends in FinTech. In detail, the included scientific papers cover financial mathematics and FinTech, presenting the innovative mathematical models and state-of-the-art technologies such as deep learning, with the aim to improve the financial analysis and decision-making and enhance the quality of financial services and risk control. The variety of the papers delivers added value for both scholars and practitioners where they will find perfect integration of elegant mathematical models and up-to-date data mini...
Advanced Manufacturing Methods
Advanced Manufacturing Methods: Smart Processes and Modeling for Optimization describes developments in advanced manufacturing processes and applications considering typical and advanced materials. It helps readers implement manufacturing 4.0 production techniques and highlights why a consolidated source and robust platform are necessary for implementing machine learning processes in the manufacturing sector. Discusses the industrial impact of manufacturing process Provides novel fundamental manufacturing solutions Presents the various aspects of applications in advanced materials in correlation of physical properties with macro-, micro- and nanostructures Reviews both classical and artificial manufacturing when applied with typical and novel innovative materials Aimed at those working in manufacturing, mechanical and optimization of manufacturing processes, this work provides readers with a comprehensive view of current development in, and applications of, advanced manufacturing.
Number Theory for the Millennium III
Building on the tradition of an outstanding series of conferences at the University of Illinois at Urbana-Champaign, the organizers attracted an international group of scholars to open the new Millennium with a conference that reviewed the current state of number theory research and pointed to future directions in the field. The conference was the largest general number theory conference in recent history, featuring a total of 159 talks, with the plenary lectures given by George Andrews, Jean Bourgain, Kevin Ford, Ron Graham, Andrew Granville, Roger Heath-Brown, Christopher Hooley, Winnie Li, Kumar Murty, Mel Nathanson, Ken Ono, Carl Pomerance, Bjorn Poonen, Wolfgang Schmidt, Chris Skinner, K. Soundararajan, Robert Tijdeman, Robert Vaughan, and Hugh Williams. The Proceedings Volumes of the conference review some of the major number theory achievements of this century and to chart some of the directions in which the subject will be heading during the new century. These volumes will serve as a useful reference to researchers in the area and an introduction to topics of current interest in number theory for a general audience in mathematics.
Number Theory for the Millennium II
Building on the tradition of an outstanding series of conferences at the University of Illinois at Urbana-Champaign, the organizers attracted an international group of scholars to open the new Millennium with a conference that reviewed the current state of number theory research and pointed to future directions in the field. The conference was the largest general number theory conference in recent history, featuring a total of 159 talks, with the plenary lectures given by George Andrews, Jean Bourgain, Kevin Ford, Ron Graham, Andrew Granville, Roger Heath-Brown, Christopher Hooley, Winnie Li, Kumar Murty, Mel Nathanson, Ken Ono, Carl Pomerance, Bjorn Poonen, Wolfgang Schmidt, Chris Skinner, K. Soundararajan, Robert Tijdeman, Robert Vaughan, and Hugh Williams. The Proceedings Volumes of the conference review some of the major number theory achievements of this century and to chart some of the directions in which the subject will be heading during the new century. These volumes will serve as a useful reference to researchers in the area and an introduction to topics of current interest in number theory for a general audience in mathematics.
