Interactions Between Group Theory Symmetry And Cryptology
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Interactions between Group Theory, Symmetry and Cryptology
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
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
Author: Md Rasid Ali
language: en
Publisher: Orange Education Pvt Ltd
Release Date: 2025-01-15
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