Preliminaries β 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 […]
Elliptic curves over finite fields
The discrete logarithm problem β Public-Key Cryptography
7.2.2 The discrete logarithm problem If g is an element of a group πΎ with operation β, we can define powers of g by writing […]
Finite fields β Public-Key Cryptography
7.6 Finite fields Fields are mathematical structures in which the basic arithmetic rules that we are used to hold true: in a field, we can […]
The encryption function β 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 Aliceβs public key PKAlice […]
Security of the RSA algorithm β Public-Key Cryptography
7.8 Security of the RSA algorithm The security of the RSA algorithm relies on the following three assumptions: We will discuss each of these assumptions […]
Authenticity of public keys β Public-Key Cryptography
7.8.3 Authenticity of public keys Another way for Mallory to attack the RSA cryptoystem is to tamper with Aliceβs public key. More specifically, Mallory might […]
Supported groups β 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 […]
Finite Field Diffie-Hellman in TLS β Public-Key Cryptography
7.10.3 Finite Field Diffie-Hellman in TLS When finite field groups are used, server Alice and client Bob execute the conventional Diffie-Hellman key agreement protocol as […]
Hybrid encryption β 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 […]
What are elliptic curves? β 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 […]