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

16.1 Preliminaries

According to the American security researchers David McGrew and John Viega, ”the Galois/Counter Mode is a block cipher mode of operation that uses universal hashing over a binary Galois field to provide authenticated encryption [114].”

Before studying the internals of the algorithm, we need to quickly cover two mathematical aspects: the finite field used by GCM and the way multiplication is done in that finite field.

16.1.1 The Galois field 𝔽2128

GCM uses multiplication over a finite field. In mathematics, finite fields are also referred to as Galois fields in honor of the 19th-century French mathematician Evariste Galois, hence the name Galois counter mode.

We have already encountered finite fields in section 7.6 Finite Fields in Chapter 7, Public-Key Cryptography. You may go back to that section to refresh your memory, but we are repeating the basic facts here for your convenience.

The field used in GCM has 2128 elements, which...