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 […]
Authenticity of public keys
Groups – Public-Key Cryptography
7.2 Groups Groups are the most basic mathematical structure in which public-key cryptography can take place. So, let’s plunge right into the math and explain […]
Finite fields – 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 […]
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 RSA algorithm – Public-Key Cryptography
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 […]
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, […]
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 […]
Finite Field Diffie-Hellman in TLS – 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 – 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 […]
Elliptic curves as abelian groups – Elliptic Curves
8.2 Elliptic curves as abelian groups Two points P and Q on a smooth elliptic curve E in reduced Weierstrass form can be added to […]