The Syntax of Encryption

An encryption scheme is defined by three algorithms Gen, Enc, and Dec, as well as aspecification of message space $\mathcal{M}$ with $|\mathcal{M}| > 1$

Gen

The key-generation algorithm Gen is a probabilistic algorithm that outputs a key $k$ chosen according some distribution.

Caesar's cipher

Encryption:

Shift the letters of the alphabet 3 places forward

There is no key because the encryption method is fixed.

The shift cipher

The shift cipher can be viewed as a keyed variant of Caesar's cipher.