Preliminaries – Public-Key Cryptography
7.1 Preliminaries Recall our earlier definition of a symmetric cryptosystem from Chapter 4, Encryption and Decryption. A symmetric cryptosystem has the following ingredients: Instead of […]
Security of the RSA algorithm
Authenticity of public keys – Public-Key Cryptography
7.4.3 Authenticity of public keys If Alice and Bob do not ensure that their public keys are authentic or do not verify their respective identities, […]
Key pair generation – Public-Key Cryptography
7.7.2 Key pair generation Alice generates her RSA key pair with the following steps: as a public key. Keep the number secret, along with p,q, […]
Authenticity of public keys – Public-Key Cryptography
7.8.3 Authenticity of public keys Another way for Mallory to attack the RSA cryptoystem is to tamper with Alice’s public key. More specifically, Mallory might […]
The Station-to-Station (STS) protocol – Public-Key Cryptography
7.9.1 The Station-to-Station (STS) protocol A simple example that nicely illustrates fundamental design principles of an authenticated key agreement protocol is the Station-to-Station (STS) protocol […]
Public-key cryptography in TLS 1.3 – Public-Key Cryptography
7.10 Public-key cryptography in TLS 1.3 Equipped with the mathematical background on public-key cryptography, we can now explore how it is applied in TLS 1.3. […]
Hybrid encryption – Public-Key Cryptography
7.11.2 Hybrid encryption A hybrid encryption scheme is a specific type of hybrid cryptosystem that allows Alice and Bob to securely encrypt data they want […]
Smoothness – Elliptic Curves
8.1.2 Smoothness Before we can start defining a group operation on the points of an elliptic curve, we need to add one requirement: The curve […]
Projective coordinates – Elliptic Curves
8.1.3 Projective coordinates In order to get to grips with the mysterious point at infinity O, we need to extend the set of points that […]
Explicit formulae – Elliptic Curves
8.2.2 Explicit formulae The geometrical viewpoint is nice to get an intuitive picture of point addition, but in order to actually implement things on a […]