Editing ElGamal encryption (section)

=== Key generation ===
The first party, Alice, generates a key pair as follows:

* Generate an efficient description of a [[cyclic group]] <math>G\,</math> of [[order (group theory)|order]] <math>q\,</math> with [[generating set of a group|generator]] <math>g</math>.  Let <math>e</math> represent the identity element of <math>G</math>.
*: It is not necessary to come up with a group and generator for each new key. Indeed, one may expect a specific implementation of ElGamal to be hardcoded to use a specific group, or a group from a specific suite. The choice of group is mostly about how large keys you want to use.
* Choose an integer <math>x</math> randomly from <math>\{1, \ldots, q-1\}</math>.
* Compute <math>h := g^x</math>.
* The '''[[public key]]''' consists of the values <math>(G,q,g,h)</math>. Alice publishes this public key and retains <math>x</math> as her '''private key''', which must be kept secret.