Interactions Between Group Theory Symmetry And Cryptology
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Interactions Between Group Theory Symmetry And Cryptology
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Author : María Isabel González Vasco
language : en
Publisher: MDPI
Release Date : 2020-04-22
Interactions Between Group Theory Symmetry And Cryptology written by María Isabel González Vasco and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-22 with Mathematics categories.
Cryptography lies at the heart of most technologies deployed today for secure communications. At the same time, mathematics lies at the heart of cryptography, as cryptographic constructions are based on algebraic scenarios ruled by group or number theoretical laws. Understanding the involved algebraic structures is, thus, essential to design robust cryptographic schemes. This Special Issue is concerned with the interplay between group theory, symmetry and cryptography. The book highlights four exciting areas of research in which these fields intertwine: post-quantum cryptography, coding theory, computational group theory and symmetric cryptography. The articles presented demonstrate the relevance of rigorously analyzing the computational hardness of the mathematical problems used as a base for cryptographic constructions. For instance, decoding problems related to algebraic codes and rewriting problems in non-abelian groups are explored with cryptographic applications in mind. New results on the algebraic properties or symmetric cryptographic tools are also presented, moving ahead in the understanding of their security properties. In addition, post-quantum constructions for digital signatures and key exchange are explored in this Special Issue, exemplifying how (and how not) group theory may be used for developing robust cryptographic tools to withstand quantum attacks.
Interactions Between Group Theory Symmetry And Cryptology
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Author : María Isabel González Vasco
language : en
Publisher:
Release Date : 2020
Interactions Between Group Theory Symmetry And Cryptology written by María Isabel González Vasco and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Mathematics categories.
Cryptography lies at the heart of most technologies deployed today for secure communications. At the same time, mathematics lies at the heart of cryptography, as cryptographic constructions are based on algebraic scenarios ruled by group or number theoretical laws. Understanding the involved algebraic structures is, thus, essential to design robust cryptographic schemes. This Special Issue is concerned with the interplay between group theory, symmetry and cryptography. The book highlights four exciting areas of research in which these fields intertwine: post-quantum cryptography, coding theory, computational group theory and symmetric cryptography. The articles presented demonstrate the relevance of rigorously analyzing the computational hardness of the mathematical problems used as a base for cryptographic constructions. For instance, decoding problems related to algebraic codes and rewriting problems in non-abelian groups are explored with cryptographic applications in mind. New results on the algebraic properties or symmetric cryptographic tools are also presented, moving ahead in the understanding of their security properties. In addition, post-quantum constructions for digital signatures and key exchange are explored in this Special Issue, exemplifying how (and how not) group theory may be used for developing robust cryptographic tools to withstand quantum attacks.
Hands On Cryptography With Python
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Author : Md Rasid Ali
language : en
Publisher: Orange Education Pvt Ltd
Release Date : 2025-01-15
Hands On Cryptography With Python written by Md Rasid Ali and has been published by Orange Education Pvt Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-15 with Computers categories.
TAGLINE Master Cryptography with Python: From History to Real-World Implementation. KEY FEATURES ● Learn by building encryption algorithms and secure systems using Python. ● Master everything from basic ciphers to advanced cryptographic solutions. ● Develop the ability to identify and address vulnerabilities in encryption systems. DESCRIPTION Cryptography is the backbone of modern digital security, and Python makes it accessible for everyone. Hands-on Cryptography with Python takes readers from foundational concepts to advanced cryptographic systems, equipping them with both theoretical understanding and practical implementation skills using Python. You’ll begin with setting up the platform and Installation and move on to understanding the basics of cryptography—exploring classic ciphers, their evolution, and their role in secure communication. Next, you’ll advance to Symmetric Key Cryptography and Asymmetric Key Cryptography, learning how to implement encryption algorithms step-by-step with Python. As you progress, you’ll dive into essential cryptographic components like Hashing and Message Integrity, enabling you to safeguard data and verify its authenticity. The book then introduces miscellaneous cryptographic schemes and highlights the principle that “Security is Only as Strong as the Weakest Link”, encouraging you to identify and address vulnerabilities. Toward the final stages, you’ll gain hands-on expertise in TLS Communication, the backbone of secure data exchange on the web. The journey culminates with an exploration of current trends in cryptography, including lightweight cryptography and post-quantum solutions, ensuring you stay ahead in this ever-evolving field. WHAT WILL YOU LEARN ● Understand cryptographic techniques from classical to modern approaches. ● Implement symmetric and asymmetric encryption using Python. ● Design secure systems using hashing and authentication protocols. ● Analyze and apply cryptographic algorithms to security challenges. ● Explore lightweight cryptography and post-quantum solutions. ● Integrate cryptography into IoT and resource-constrained devices. WHO IS THIS BOOK FOR? This book is tailored for security professionals, software developers, researchers and students seeking to implement secure cryptography and secure encryption in real-world applications. It’s also ideal for IoT and embedded systems engineers designing secure solutions for resource-constrained environments, as well as enthusiasts eager to learn about modern cryptography and its practical applications. TABLE OF CONTENTS 1. Platform Setup and Installation 2. Introduction to Cryptography 3. Symmetric Key Cryptography 4. Asymmetric Key Cryptography 5. Hashing 6. Message Integrity 7. Miscellaneous Crypto Schemes 8. Security is Only as Strong as the Weakest Link 9. TLS Communication 10. Latest Trends in Cryptography Index
Basics Of Representation Theory
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Author : Udayan Bhattacharya
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Basics Of Representation Theory written by Udayan Bhattacharya and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
Delve into the captivating world of "Basics of Representation Theory," a comprehensive guide designed for students, researchers, and enthusiasts eager to explore the intricate symmetries and structures that underpin modern mathematics. Our book offers a detailed introduction to foundational concepts, providing a solid understanding of group actions, linear representations, and character theory. From there, it explores the algebraic structures of irreducible representations, breaking down the decomposition into irreducible components and examining the properties of characters. Readers will journey through diverse topics, including the representation theory of symmetric groups, Lie groups, and algebraic groups, as well as advanced topics such as the representation theory of finite groups, the Langlands program, and applications in quantum mechanics and number theory. With a wealth of examples, illustrations, and exercises, "Basics of Representation Theory" ensures a hands-on approach to learning, encouraging practical exploration and problem-solving. The book also includes numerous references and further reading suggestions for those who wish to delve deeper into specific topics. Written in a clear and accessible style, this book caters to all levels, from undergraduate students encountering representation theory for the first time to experienced researchers seeking fresh insights. With its comprehensive coverage and diverse applications, "Basics of Representation Theory" is an invaluable resource for anyone interested in the beauty and depth of this field.
Essentials Of Abstract Algebra
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Author : Sachin Nambeesan
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Essentials Of Abstract Algebra written by Sachin Nambeesan and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
"Essentials of Abstract Algebra" offers a deep exploration into the fundamental structures of algebraic systems. Authored by esteemed mathematicians, this comprehensive guide covers groups, rings, fields, and vector spaces, unraveling their intricate properties and interconnections. We introduce groups, exploring their diverse types, from finite to infinite and abelian to non-abelian, with concrete examples and rigorous proofs. Moving beyond groups, we delve into rings, explaining concepts like ideals, homomorphisms, and quotient rings. The text highlights the relevance of ring theory in number theory, algebraic geometry, and coding theory. We also navigate fields, discussing field extensions, Galois theory, and algebraic closures, and exploring connections between fields and polynomial equations. Additionally, we venture into vector spaces, examining subspaces, bases, dimension, and linear transformations. Throughout the book, we emphasize a rigorous mathematical foundation and intuitive understanding. Concrete examples, diagrams, and exercises enrich the learning experience, making abstract algebra accessible to students, mathematicians, and researchers. "Essentials of Abstract Algebra" is a timeless resource for mastering the beauty and power of algebraic structures.
Group Theory
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Author : Parthiban Srinivasan
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Group Theory written by Parthiban Srinivasan and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
"Group Theory: Foundations and Applications" is a comprehensive guide designed to demystify the fascinating subject of Group Theory. We explore this foundational branch of mathematics that examines symmetry and structure through the study of mathematical groups. In this book, we take readers on a journey through the fundamental concepts and applications of Group Theory, starting with the basics and gradually building up to more advanced topics. We begin by introducing essential definitions and properties of groups, exploring their algebraic structures and fundamental theorems. From there, we delve into group homomorphisms, isomorphisms, and subgroups, providing clear explanations and illustrative examples to aid understanding. As we progress, we explore various types of groups, including permutation groups, cyclic groups, and symmetry groups, showcasing their applications in areas such as chemistry, physics, cryptography, and computer science. Throughout the book, we emphasize Group Theory's importance in elucidating patterns, symmetries, and relationships in mathematical structures and real-world phenomena. With a balance of theory, examples, and exercises, "Group Theory: Foundations and Applications" engages and empowers undergraduate students. Whether you are a mathematics major, a student in a related field, or simply curious about the beauty of mathematical structures, this book will be your comprehensive guide to understanding Group Theory and its myriad applications.
Symmetries Unveiled
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Author : Oliver Vella
language : en
Publisher: eBookIt.com
Release Date : 2025-02-27
Symmetries Unveiled written by Oliver Vella and has been published by eBookIt.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-27 with Mathematics categories.
Exploring the Mysteries of Representation Theory Dive into the fascinating universe of symmetries and representations, where mathematics unravels the secrets of the universe. Symmetries Unveiled: A Journey Through Representation Theory invites readers on a thrilling expedition through the intricate landscape of mathematical theory and its profound impact on science. As you embark on this mathematical voyage, you'll uncover foundational concepts and historical development behind representation theory. From the elegant symmetries of groups to the groundbreaking applications of linear representations, this book is your gateway to a deeper understanding of the subject. Through chapters dedicated to Lie algebras, root systems, and quantum groups, the narrative weaves a tapestry of knowledge that connects abstract theory with real-world applications. Imagine navigating the compelling world of Kac-Moody algebras, discovering the role of crystal bases, and unlocking the mysteries of non-linear realisations. Each chapter promises to ignite curiosity with insights into symmetries in quantum mechanics and their implications in modern physics. Whether you're captivated by symmetry breaking or intrigued by the concept of duality, this book offers a profound exploration of these topics and more. Symmetries Unveiled is not just a book for mathematicians; it's a treasure trove for anyone passionate about the interplay between theory and application in theoretical physics. With chapters on computational approaches, educational techniques, and interdisciplinary impacts, it also serves as a comprehensive guide for educators and researchers alike. The culmination of the journey is an exploration of open problems and philosophical insights, paving the way for future exploration and discovery. Join this intellectual adventure and let Symmetries Unveiled transform your understanding of the mathematical principles that underpin the very fabric of reality.
Abstract Algebra Group Theory
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Author : N.B. Singh
language : en
Publisher: N.B. Singh
Release Date :
Abstract Algebra Group Theory written by N.B. Singh and has been published by N.B. Singh this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
Geometric Methods In Signal And Image Analysis
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Author : Hamid Krim
language : en
Publisher: Cambridge University Press
Release Date : 2015-06-18
Geometric Methods In Signal And Image Analysis written by Hamid Krim and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-18 with Computers categories.
A comprehensive guide to modern geometric methods for signal and image analysis, from basic principles to state-of-the-art concepts and applications.
Theory Of Quantum Computation Communication And Cryptography
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Author : Kazuo Iwama
language : en
Publisher: Springer
Release Date : 2013-01-05
Theory Of Quantum Computation Communication And Cryptography written by Kazuo Iwama and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-05 with Computers categories.
This book constitutes revised selected papers from the 7th Conference on Theory of Quantum Computation, Communication, and Cryptography, TQC 2012, held in Tokyo, Japan, in May 2012. The 12 papers presented were carefully reviewed and selected for inclusion in this book. They contain original research on the rapidly growing, interdisciplinary field of quantum computation, communication and cryptography. Topics addressed are such as quantum algorithms, quantum computation models, quantum complexity theory, simulation of quantum systems, quantum programming languages, quantum cryptography, quantum communication, quantum estimation, quantum measurement, quantum tomography, completely positive maps, decoherence, quantum noise, quantum coding theory, fault-tolerant quantum computing, entanglement theory, and quantum teleportation.