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 […]
Key pair generation
The Diffie-Hellman key-exchange protocol – Public-Key Cryptography
7.3 The Diffie-Hellman key-exchange protocol Alice and Bob communicate over an insecure channel. They can establish a shared secret K using the following protocol steps […]
Fields of order pk – Public-Key Cryptography
7.6.2 Fields of order pk Are there any other finite fields than 𝔽p? It seems that the requirements that the order of the field must […]
The encryption function – Public-Key Cryptography
7.7.3 The encryption function In order to send an encrypted message to Alice, Bob needs to obtain an authentic copy of Alice’s public key PKAlice […]
The Station-to-Station (STS) protocol 2 – Public-Key Cryptography
If the signature verification is successful, Alice generates her own signature sigA(h(gα|gβ)), encrypts it using the shared secret key K, and sends the result to […]
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 […]
Supported groups – Public-Key Cryptography
7.10.2 Supported groups When client Bob starts a TLS handshake with server Alice and wishes to use the ECDHE or DHE key agreement protocol, he […]
What are elliptic curves? – Elliptic Curves
8.1 What are elliptic curves? Historically, elliptic curves are rooted in so-called Diophantine equations, named after ancient Greek mathematician Diophantus of Alexandria. Diophantine equations are […]
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 […]