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TLS Cryptography In-Depth

TLS Cryptography In-Depth

By : Dr. Paul Duplys, Dr. Roland Schmitz
4.8 (4)
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TLS Cryptography In-Depth

TLS Cryptography In-Depth

4.8 (4)
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)
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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

7.8 Security of the RSA algorithm

The security of the RSA algorithm relies on the following three assumptions:

  • The factoring problem is hard for the given public modulus n

  • The RSA problem is hard

  • The public keys of Alice and Bob are authentic

We will discuss each of these assumptions in turn.

7.8.1 The factoring problem

If an attacker manages to compute the two prime factors p and q of the public modulus n, they can repeat the steps taken by Alice when she computed her key pair. In particular, an attacker could compute Alice’s secret key and compromise the whole system. Therefore, the security of the RSA cryptosystem is crucially based on the intractability of the integer factorization problem, which is in general defined as follows:

Given a positive integer n, find its prime factors p1 to pk such that

 e1 e2 ek n = p1 × p2 × ...× pk ,

where pi are pairwise distinct primes.

The fastest algorithm to factorize semiprimes, which are numbers of the form n = p q with p and q primes of approximately equal...

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