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 […]
Projective coordinates
Security of Diffie-Hellman key exchange – Public-Key Cryptography
7.4 Security of Diffie-Hellman key exchange The security of the Diffie-Hellman protocol relies on the following three assumptions: We will discuss each of these assumptions […]
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 […]
Security of the RSA algorithm – 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 […]
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 […]
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. […]
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 […]
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 […]
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 […]
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 […]