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

7.7 The RSA algorithm

The RSA algorithm is named after its inventors, Ron Rivest, Adi Shamir, and Len Adleman (see Chapter 1, The Role of Cryptography in a Connected World, for a photo). Its trapdoor mechanism is based on the assumption that factoring, that is, finding the prime factors of a large integer n, is hard, while the inverse problem, namely multiplying prime factors to get n, is easy. While this trapdoor is certainly much easier to understand than the discrete-logarithm problem, understanding how exactly it can be used to realize a public-key cryptosystem requires a bit of math (again). We start by defining an odd-looking function.

7.7.1 Euler’s totient function

No doubt you are familiar with prime numbers. To recap, p is a prime number if it has no divisors other than 1 and p. For two integer numbers a and b, we can always find a greatest common divisor c, or c = gcd(a,b) for short. c is the greatest integer that divides both a and b. For example, 3 is the greatest...