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

7.4 Security of Diffie-Hellman key exchange

The security of the Diffie-Hellman protocol relies on the following three assumptions:

  • The discrete logarithm problem is hard in the chosen group 𝔾

  • The Diffie-Hellman problem is hard in the chosen group 𝔾

  • The public keys of Alice and Bob are authentic

We will discuss each of these assumptions in turn.

7.4.1 Discrete logarithm problem

If Eve is passively eavesdropping on the protocol exchange shown in Figure 7.1, she sees the generator g and the public key values A and B coming from Alice and Bob, respectively. This means if Eve could efficiently solve the discrete logarithm problem in group 𝔾, she could recover both private keys α and β. Armed with this knowledge, she could also compute the shared secret of Alice and Bob.

As discussed previously, we must ensure that the discrete logarithm problem is hard in 𝔾, so that an attacker cannot derive the private keys or the shared secret. For 𝔽...