10 Examples Cryptography
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An Introduction to Number Theory with Cryptography
Number theory has a rich history. For many years it was one of the purest areas of pure mathematics, studied because of the intellectual fascination with properties of integers. More recently, it has been an area that also has important applications to subjects such as cryptography. An Introduction to Number Theory with Cryptography presents number
Cryptography for Secure Encryption
Author: Robert G. Underwood
language: en
Publisher: Springer Nature
Release Date: 2022-06-03
This text is intended for a one-semester course in cryptography at the advanced undergraduate/Master's degree level. It is suitable for students from various STEM backgrounds, including engineering, mathematics, and computer science, and may also be attractive for researchers and professionals who want to learn the basics of cryptography. Advanced knowledge of computer science or mathematics (other than elementary programming skills) is not assumed. The book includes more material than can be covered in a single semester. The Preface provides a suggested outline for a single semester course, though instructors are encouraged to select their own topics to reflect their specific requirements and interests. Each chapter contains a set of carefully written exercises which prompts review of the material in the chapter and expands on the concepts. Throughout the book, problems are stated mathematically, then algorithms are devised to solve the problems. Students are tasked to write computer programs (in C++ or GAP) to implement the algorithms. The use of programming skills to solve practical problems adds extra value to the use of this text. This book combines mathematical theory with practical applications to computer information systems. The fundamental concepts of classical and modern cryptography are discussed in relation to probability theory, complexity theory, modern algebra, and number theory. An overarching theme is cyber security: security of the cryptosystems and the key generation and distribution protocols, and methods of cryptanalysis (i.e., code breaking). It contains chapters on probability theory, information theory and entropy, complexity theory, and the algebraic and number theoretic foundations of cryptography. The book then reviews symmetric key cryptosystems, and discusses one-way trap door functions and public key cryptosystems including RSA and ElGamal. It contains a chapter on digital signature schemes, including material on message authentication and forgeries, and chapters on key generation and distribution. It contains a chapter on elliptic curve cryptography, including new material on the relationship between singular curves, algebraic groups and Hopf algebras.
Cryptography Simply In Depth
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. While extremely useful, cryptography is also highly brittle. The most secure cryptographic system can be rendered completely insecure by a single specification or programming error. No amount of unit testing will uncover a security vulnerability in a cryptosystem. Instead, to argue that a cryptosystem is secure, we rely on mathematical modeling and proofs to show that a particular system satisfies the security properties attributed to it. We often need to introduce certain plausible assumptions to push our security arguments through. This book is about exactly that: constructing practical cryptosystems for which we can argue security under plausible assumptions. The book covers many constructions for different tasks in cryptography. For each task we define a precise security goal that i aim to achieve and then present constructions that achieve the required goal. To analyze the constructions, we develop a unified framework for doing cryptographic proofs. A reader who masters this framework will be capable of applying it to new constructions that may not be covered in the book. Throughout the book i presented many case studies to survey how deployed systems operate. I described common mistakes to avoid as well as attacks on real-world systems that illustrate the importance of rigor in cryptography. I ended every chapter with a fun application that applies the ideas in the chapter in some unexpected way.