Book Image

TLS Cryptography In-Depth

By : Dr. Paul Duplys, Dr. Roland Schmitz
Book Image

TLS Cryptography In-Depth

By: Dr. Paul Duplys, Dr. Roland Schmitz

Overview of this book

TLS is the most widely used cryptographic protocol today, enabling e-commerce, online banking, and secure online communication. Written by Dr. Paul Duplys, Security, Privacy & Safety Research Lead at Bosch, and Dr. Roland Schmitz, Internet Security Professor at Stuttgart Media University, this book will help you gain a deep understanding of how and why TLS works, how past attacks on TLS were possible, and how vulnerabilities that enabled them were addressed in the latest TLS version 1.3. By exploring the inner workings of TLS, you’ll be able to configure it and use it more securely. Starting with the basic concepts, you’ll be led step by step through the world of modern cryptography, guided by the TLS protocol. As you advance, you’ll be learning about the necessary mathematical concepts from scratch. Topics such as public-key cryptography based on elliptic curves will be explained with a view on real-world applications in TLS. With easy-to-understand concepts, you’ll find out how secret keys are generated and exchanged in TLS, and how they are used to creating a secure channel between a client and a server. By the end of this book, you’ll have the knowledge to configure TLS servers securely. Moreover, you’ll have gained a deep knowledge of the cryptographic primitives that make up TLS.
Table of Contents (30 chapters)
1
Part I Getting Started
8
Part II Shaking Hands
16
Part III Off the Record
22
Part IV Bleeding Hearts and Biting Poodles
27
Bibliography
28
Index

8.1 What are elliptic curves?

Historically, elliptic curves are rooted in so-called Diophantine equations, named after ancient Greek mathematician Diophantus of Alexandria. Diophantine equations are polynomial equations in two or more unknowns for which only integer solutions are of interest.

In the 19th century, these studies became more formalized and were extended to so called algebraic curves, which are the set of zeros of a polynomial of two variables in a plane. Circles, as defined as the zeros of

 2 2 2 x + y − R

and ellipses, defined as the zeros of

 2 2 x--+ y--− 1 a2 b2

are the most common examples of algebraic curves. However, elliptic curves are not ellipses. They arose from the study of so-called elliptic integrals, by which the arc length of ellipses is computed, and were intensively studied by pure mathematicians in the 19th and early 20th century. They are characterized by their amazing property of possessing a way to add curve points, so that the result is another point on the curve.

In 1985, Victor Miller...