Asymmetric cryptosystems

Also: public-key cryptography.

An asymmetric cryptosystem defines the following operations:

• Setup: Any operation that describes prerequisites for the cryptosystem, for example the construction of a special group.
• KeyGen\((\lambda) \mapsto \langle \mathit{pk}, \mathit{sk} \rangle\): Generates a public-secret key pair used to encrypt and decrypt.
• Encrypt\((m, \mathit{pk}) \mapsto c\): Encrypts a message using the public key into a ciphertext.
• Decrypt\((c, \mathit{pk}) \mapsto m\): Decrypts a ciphertext using the secret key to recover the plaintext.

Symbol definitions

• \(\lambda\) - security parameter
• \(\mathit{pk}\) - public key
• \(\mathit{sk}\) - secret key
• \(m\) - plaintext
• \(c\) - ciphertext