Implementation flaws, weak passwords or negligent users. In practice, attacks often exploit protocol or That real-world security is a complex process in which cryptography contributes “only” Security threats is driving the trend to protect data whenever possible, be it for storage or during transmission over networks. Thirdly, cryptography has become a key technology that is used ubiquitously inĬomputer systems from small devices to large servers and networks. Cryptography, which we use as an umbrella termįor the field including cryptanalysis, is linked to aspects of discrete mathematics, number theory, algebra, probability theory, statistics, information and coding theory. Secondly, cryptography is closely connected to several fields of mathematics andĬomputer science, providing interesting applications for many theoretical results and The subject now includes all mathematical techniques Modern cryptography goes beyond confidentiality, also addressing aspects such as data integrity, authentication, non-repudiationĪnd other security objectives. Since then, the techniques have been adapted to progress in cryptanalysisĪnd to the computing power available. The design of new ciphers and the capability to analyze and break them co-evolved Protection against exposure was sometimes dubious and many ciphers were broken. Encryption techniques have been used since ancient times, but the Why is cryptography interesting? Firstly, cryptography is a classical subject with a fascinating history. Efficiency and Security of Elliptic Curve Cryptography Weierstrass Equations and Elliptic Curvesġ2.3. Definitions and Security Requirementsġ2.1. Public-Key Encryption and the RSA Cryptosystemġ1.1. Definitions and Security RequirementsĨ.1. ∞ The paper used in this book is acid-free and falls within the guidelinesĮstablished to ensure permanence and durability.Įncryption Schemes and Definitions of Securityħ.1. More information, please visit Send requests for translation rights and licensed reprints to 2019 by the author. To reuse portions of AMS publication content are handled by the Copyright Clearance Center.
Is permitted only under license from the American Mathematical Society. Republication, systematic copying, or multiple reproduction of any material in this publication Reviews, provided the customary acknowledgment of the source is given. Permission is granted to quote brief passages from this publication in Individual readers of this publication, and nonprofit libraries actingįor them, are permitted to make fair use of the material, such as to copy select pages for use fields and commutative rings (number-theoretic aspects) – Algebraic coding theory cryptography. msc | Quantum theory –Īxiomatics, foundations, philosophy – Quantum cryptography.
msc | Computer science – Theory of data – Data encryption. |ĪMS: Information and communication, circuits – Communication, information – Cryptography. Title: A course in cryptography / Heiko Knospe.ĭescription: Providence, Rhode Island: American Mathematical Society, | Series: Pure andĪpplied undergraduate texts volume 40 | Includes bibliographical references and index.
Library of Congress Cataloging-in-Publication Data Primary 94A60 įor additional information and updates on this book, visit Sally, Jr.Ģ-color cover: PMS 432 (Gray) and PMS 300 (Blue)Ģ010 Mathematics Subject Classification.
This series was founded by the highly respected Lattice-based and code-based cryptosystems. The current developments in post-quantumĬryptography are also explored, with separate chapters on quantum computing, Message authentication codes, public-key encryption, key establishment, digital Schemes are covered, including block ciphers, stream ciphers, hash functions, The text provides rigorous definitionsĪnd follows the provable security approach. The mathematical foundations in algebra, number theory and probability are presented with aįocus on their cryptographic applications.
This book provides a compact course in modern cryptography. Suitable as a textbook for undergraduate and graduate courses in cryptography The text requires only a first-year course in mathematics (calculus and linearĪlgebra) and is also accessible to computer scientists and engineers.
Mathematics and the modern approach to cryptography and security prepare A special focus is on algebraic structures, which are used in manyĬryptographic constructions and also in post-quantum systems. Many examples, figures and exercises, as well as SageMath (Python) computerĬode, help the reader to understand the concepts and applications of modernĬryptography.