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                <text>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, the author introduces the theory and technology of LWE distribution, LWE ciphers, and homomorphic encryption in detail. When using random analysis tools, there is a problem of "ambiguity" in both definition and algorithm. The greatest feature of this book is its use of probability distribution to carry out rigorous mathematical definitions and mathematical demonstrations for various unclear or imprecise expressions, so as to make it a rigorous theoretical system for classroom teaching and dissemination. Chapters 5 and 7 further expand and improve the theory of cyclic lattices, ideal lattices, and generalized NTRU cryptography.&#13;
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                <text>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.&#13;
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                <text>Cryptography is an indispensable tool used to protect information in computing systems. It is used everywhere and by billions of people worldwide on a daily basis. It is used to protect data at rest and data in motion. Cryptographic systems are an integral part of standard protocols, most notably the Transport Layer Security (TLS) protocol, making it relatively easy to incorporate strong encryption into a wide range of applications.&#13;
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                <text>Information theory deals with mathematical laws that govern the flow, representation, and transmission of information, just as the field of physics concerns laws that govern the behavior of the physical universe. The foundation was made in the context of communication while characterizing the fundamental limits of communication and offering codes (sometimes called algorithms) to achieve them.&#13;
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The most significant achievement of the field is the invention of digital communication, which forms the basis of our daily-life digital products such as smartphones, laptops, and any IoT devices. Recently it has also found important roles in a spotlight field that has been revolutionized during the past decades: data science.&#13;
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This book aims at demonstrating modern roles of information theory in a widening array of data science applications. The first and second parts of the book cover the core concepts of information theory: basic concepts on several key notions and celebrated source and channel coding theorems, which concern the fundamental limits of communication. The last part focuses on applications that arise in data science, including social networks, ranking, and machine learning.&#13;
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The book is written as a text for senior undergraduate and graduate students working on information theory and communications, and it should also prove to be a valuable reference for professionals and engineers from these fields.</text>
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