Elliptic Curve Cryptography for Developers

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 conceptsImplementing efficient digital signature algorithmsState of the art zero-knowledge proofsBlockchain applications with ECC-backed securityThe 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.About the technologyThe 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 bookElliptic 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 insideEfficient digital signature algorithmsZero-knowledge proofsECC security for blockchain applicationsAbout the readerReaders need to understand basic calculus. Examples in C.About the authorMichael 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 Contents1 Pairings over elliptic curves in cryptographyPart 12 Description of finite field mathematics3 Explaining the core of elliptic curve mathematics4 Key exchange using elliptic curves5 Prime field elliptic curve digital signatures explained6 Finding good cryptographic elliptic curvesPart 27 Description of finite field polynomial math8 Multiplication of polynomials explained9 Computing powers of polynomials10 Description of polynomial division using Euclid’s algorithm11 Creating irreducible polynomials12 Taking square roots of polynomialsPart 313 Finite field extension curves described14 Finding low embedding degree elliptic curves15 General rules of elliptic curve pairing explained16 Weil pairing defined17 Tate pairing defined18 Exploring BLS multi-signatures19 Proving knowledge and keeping secrets: Zero knowledge using pairingsAppendix A Code and toolsAppendix B Hilbert class polynomialsAppendix C Variables list

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