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 […]
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 […]
The discrete logarithm problem – Public-Key Cryptography
7.2.2 The discrete logarithm problem If g is an element of a group 𝔾 with operation ⋆, we can define powers of g by writing […]
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 […]
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 […]
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, […]
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, […]