After two decades of research and development, elliptic curve cryptography now has widespread exposure and acceptance. Industry, banking, and government standards are in place to facilitate extensive deployment of this efficient public-key mechanism. Anchored by a comprehensive treatment of the practical aspects of elliptic curve cryptography (ECC), this guide explains the basic mathematics, describes state-of-the-art implementation methods, and presents standardized protocols for public-key encryption, digital signatures, and key establishment. In addition, the book addresses some issues that arise in software and hardware implementation, as well as side-channel attacks and countermeasures. Readers receive the theoretical fundamentals as an underpinning for a wealth of practical and accessible knowledge about efficient application. Features & Benefits: * Breadth of coverage and unified, integrated approach to elliptic curve cryptosystems * Describes important industry and government protocols, such as the FIPS 186-2 standard from the U.S. National Institute for Standards and Technology * Provides full exposition on techniques for efficiently implementing finite-field and elliptic curve arithmetic * Distills complex mathematics and algorithms for easy understanding * Includes useful literature references, a list of algorithms, and appendices on sample parameters, ECC standards, and software tools This comprehensive, highly focused reference is a useful and indispensable resource for practitioners, professionals, or researchers in computer science, computer engineering, network design, and network data security.

Make your public key protocols smaller and more secure with this accessible guide to Elliptic Curve Cryptography. Elliptic Curve Cryptography for Developers introduces the mathematics of elliptic curves—a powerful alternative to the prime number-based RSA encryption standard. You’ll learn to deliver zero-knowledge proofs and aggregated multi-signatures that are not even possible with RSA mathematics. All you need is the basics of calculus you learned in high school. Elliptic Curve Cryptography for Developers includes: • Clear, well-illustrated introductions to key ECC concepts • Implementing efficient digital signature algorithms • State of the art zero-knowledge proofs • Blockchain applications with ECC-backed security The book gradually introduces the concepts and subroutines you’ll need to master with diagrams, flow charts, and accessible language. Each chapter builds on what you’ve already learned, with step-by-step guidance until you’re ready to write embedded systems code with advanced mathematical algorithms. Purchase of the print book includes a free eBook in PDF and ePub formats from Manning Publications. About the technology The Elliptic Curve Cryptography (ECC) protocol secures everything from credit card transactions to the blockchain. With a little C code, high school calculus, and the techniques in this book, you can implement ECC cryptographic protocols that are smaller and more secure than the RSA-based systems in common use today. About the book Elliptic Curve Cryptography for Developers teaches you how ECC protocols work and how to implement them seamlessly in C code. Unlike academic cryptography books, this practical guide sticks to the minimum math and theory you need to get the job done. Author Mike Rosing illustrates each concept with clear graphics, detailed code, and hands-on exercises. As you go, you’ll practice what you learn by building two encryption systems for a blockchain application. What's inside • Efficient digital signature algorithms • Zero-knowledge proofs • ECC security for blockchain applications About the reader Readers need to understand basic calculus. Examples in C. About the author Michael Rosing’s career as a scientist, hardware engineer, and software developer includes high-energy physics, telephone switch engineering, and developing vision devices for the blind. The technical editor on this book was Mark Bissen. Table of Contents 1 Pairings over elliptic curves in cryptography Part 1 2 Description of finite field mathematics 3 Explaining the core of elliptic curve mathematics 4 Key exchange using elliptic curves 5 Prime field elliptic curve digital signatures explained 6 Finding good cryptographic elliptic curves Part 2 7 Description of finite field polynomial math 8 Multiplication of polynomials explained 9 Computing powers of polynomials 10 Description of polynomial division using Euclid’s algorithm 11 Creating irreducible polynomials 12 Taking square roots of polynomials Part 3 13 Finite field extension curves described 14 Finding low embedding degree elliptic curves 15 General rules of elliptic curve pairing explained 16 Weil pairing defined 17 Tate pairing defined 18 Exploring BLS multi-signatures 19 Proving knowledge and keeping secrets: Zero knowledge using pairings Appendix A Code and tools Appendix B Hilbert class polynomials Appendix C Variables list

This second volume addresses tremendous progress in elliptic curve cryptography since the first volume.

The discrete logarithm problem based on elliptic and hyperelliptic curves has gained a lot of popularity as a cryptographic primitive. The main reason is that no subexponential algorithm for computing discrete logarithms on small genus curves is currently available, except in very special cases. Therefore curve-based cryptosystems require much smaller key sizes than RSA to attain the same security level. This makes them particularly attractive for implementations on memory-restricted devices like smart cards and in high-security applications. The Handbook of Elliptic and Hyperelliptic Curve Cryptography introduces the theory and algorithms involved in curve-based cryptography. After a very detailed exposition of the mathematical background, it provides ready-to-implement algorithms for the group operations and computation of pairings. It explores methods for point counting and constructing curves with the complex multiplication method and provides the algorithms in an explicit manner. It also surveys generic methods to compute discrete logarithms and details index calculus methods for hyperelliptic curves. For some special curves the discrete logarithm problem can be transferred to an easier one; the consequences are explained and suggestions for good choices are given. The authors present applications to protocols for discrete-logarithm-based systems (including bilinear structures) and explain the use of elliptic and hyperelliptic curves in factorization and primality proving. Two chapters explore their design and efficient implementations in smart cards. Practical and theoretical aspects of side-channel attacks and countermeasures and a chapter devoted to (pseudo-)random number generation round off the exposition. The broad coverage of all- important areas makes this book a complete handbook of elliptic and hyperelliptic curve cryptography and an invaluable reference to anyone interested in this exciting field.

This book is dedicated to the development of a sophisticated and feature-rich Tkinter GUI that leverages Elliptic Curve Cryptography (ECC) for various cryptographic operations, including key generation, encryption, decryption, signing, and verifying data. The primary goal is to create an interactive application that allows users to perform these operations on synthetic financial data, demonstrating the practical use of ECC in securing sensitive information. The GUI is meticulously designed with multiple tabs, each corresponding to a different cryptographic function, enabling users to navigate through key generation, data encryption/decryption, and digital signature processes seamlessly. The GUI starts with the key generation tab, where users can generate ECC key pairs. These key pairs are essential for the subsequent encryption and signing operations. The GUI provides feedback on the generated keys, displaying the public and private keys in hexadecimal format. This feature is crucial for understanding the foundational role of ECC in modern cryptography, where small key sizes provide strong security. The key generation process also highlights the advantages of ECC over traditional RSA, particularly in terms of efficiency and security per bit length. In the encryption and decryption tab, the GUI enables users to encrypt synthetic financial data using the previously generated ECC keys. The encryption process is performed using AES in Cipher Feedback (CFB) mode, with the AES key derived from the ECC private key through key derivation functions. This setup showcases the hybrid approach where ECC is used for key exchange or key derivation, and AES is employed for the actual encryption of data. The GUI displays the generated ciphertext in a hexadecimal format, along with the Initialization Vector (IV) used in the encryption process, providing a clear view of how the encrypted data is structured. The signing and verifying tab demonstrates the use of ECC for digital signatures. Here, users can sign the synthetic financial data using the ECDSA (Elliptic Curve Digital Signature Algorithm), a widely recognized algorithm for ensuring data integrity and authenticity. The GUI displays the generated digital signature in hexadecimal format, offering insights into how ECC is applied in real-world scenarios like secure messaging and digital certificates. The verification process, where the signature is checked against the original data using the ECC public key, is also integrated into the GUI, emphasizing the importance of digital signatures in verifying data authenticity. The synthetic financial data used in these operations is generated within the GUI, simulating transaction records that include fields such as transaction ID, account number, amount, currency, timestamp, and transaction type. This dataset is crucial for demonstrating the encryption and signing processes in a context that mirrors real-world financial systems. By encrypting and signing this data, users can understand how ECC can be applied to protect sensitive information in financial transactions, ensuring both confidentiality and integrity. Finally, the GUI’s design incorporates user-friendly elements such as scrolled text widgets for displaying long hexadecimal outputs, entry fields for user inputs, and clear labels for guiding the user through each cryptographic operation. The application provides a comprehensive and interactive learning experience, allowing users to explore the intricacies of ECC in a controlled environment. By integrating ECC with AES for encryption and ECDSA for signing, the GUI offers a practical demonstration of how modern cryptographic techniques can be combined to secure data, making it an invaluable tool for anyone looking to understand or teach the principles of ECC-based cryptography.

Expanded into two volumes, the Second Edition of Springer’s Encyclopedia of Cryptography and Security brings the latest and most comprehensive coverage of the topic: Definitive information on cryptography and information security from highly regarded researchers Effective tool for professionals in many fields and researchers of all levels Extensive resource with more than 700 contributions in Second Edition 5643 references, more than twice the number of references that appear in the First Edition With over 300 new entries, appearing in an A-Z format, the Encyclopedia of Cryptography and Security provides easy, intuitive access to information on all aspects of cryptography and security. As a critical enhancement to the First Edition’s base of 464 entries, the information in the Encyclopedia is relevant for researchers and professionals alike. Topics for this comprehensive reference were elected, written, and peer-reviewed by a pool of distinguished researchers in the field. The Second Edition’s editorial board now includes 34 scholars, which was expanded from 18 members in the First Edition. Representing the work of researchers from over 30 countries, the Encyclopedia is broad in scope, covering everything from authentication and identification to quantum cryptography and web security. The text’s practical style is instructional, yet fosters investigation. Each area presents concepts, designs, and specific implementations. The highly-structured essays in this work include synonyms, a definition and discussion of the topic, bibliographies, and links to related literature. Extensive cross-references to other entries within the Encyclopedia support efficient, user-friendly searches for immediate access to relevant information. Key concepts presented in the Encyclopedia of Cryptography and Security include: Authentication and identification; Block ciphers and stream ciphers; Computational issues; Copy protection; Cryptanalysis and security; Cryptographic protocols; Electronic payment and digital certificates; Elliptic curve cryptography; Factorization algorithms and primality tests; Hash functions and MACs; Historical systems; Identity-based cryptography; Implementation aspects for smart cards and standards; Key management; Multiparty computations like voting schemes; Public key cryptography; Quantum cryptography; Secret sharing schemes; Sequences; Web Security. Topics covered: Data Structures, Cryptography and Information Theory; Data Encryption; Coding and Information Theory; Appl.Mathematics/Computational Methods of Engineering; Applications of Mathematics; Complexity. This authoritative reference will be published in two formats: print and online. The online edition features hyperlinks to cross-references, in addition to significant research.

Novel Algorithms and Techniques in Telecommunications, Automation and Industrial Electronics includes a set of rigorously reviewed world-class manuscripts addressing and detailing state-of-the-art research projects in the areas of Industrial Electronics, Technology and Automation, Telecommunications and Networking. Novel Algorithms and Techniques in Telecommunications, Automation and Industrial Electronics includes selected papers form the conference proceedings of the International Conference on Industrial Electronics, Technology and Automation (IETA 2007) and International Conference on Telecommunications and Networking (TeNe 07) which were part of the International Joint Conferences on Computer, Information and Systems Sciences and Engineering (CISSE 2007).

The purpose of this book is to present some of the critical security challenges in today's computing world and to discuss mechanisms for defending against those attacks by using classical and modern approaches of cryptography and other defence mechanisms. It contains eleven chapters which are divided into two parts. The chapters in Part 1 of the book mostly deal with theoretical and fundamental aspects of cryptography. The chapters in Part 2, on the other hand, discuss various applications of cryptographic protocols and techniques in designing computing and network security solutions. The book will be useful for researchers, engineers, graduate and doctoral students working in cryptography and security related areas. It will also be useful for faculty members of graduate schools and universities.

This text provides a practical survey of both the principles and practice of cryptography and network security.

The only book to provide a unified view of the interplay between computational number theory and cryptography Computational number theory and modern cryptography are two of the most important and fundamental research fields in information security. In this book, Song Y. Yang combines knowledge of these two critical fields, providing a unified view of the relationships between computational number theory and cryptography. The author takes an innovative approach, presenting mathematical ideas first, thereupon treating cryptography as an immediate application of the mathematical concepts. The book also presents topics from number theory, which are relevant for applications in public-key cryptography, as well as modern topics, such as coding and lattice based cryptography for post-quantum cryptography. The author further covers the current research and applications for common cryptographic algorithms, describing the mathematical problems behind these applications in a manner accessible to computer scientists and engineers. Makes mathematical problems accessible to computer scientists and engineers by showing their immediate application Presents topics from number theory relevant for public-key cryptography applications Covers modern topics such as coding and lattice based cryptography for post-quantum cryptography Starts with the basics, then goes into applications and areas of active research Geared at a global audience; classroom tested in North America, Europe, and Asia Incudes exercises in every chapter Instructor resources available on the book’s Companion Website Computational Number Theory and Modern Cryptography is ideal for graduate and advanced undergraduate students in computer science, communications engineering, cryptography and mathematics. Computer scientists, practicing cryptographers, and other professionals involved in various security schemes will also find this book to be a helpful reference.