Alice chooses a group of prime order p, with generator g.
Note that the depends on the order P of the local regression.
The group has a unique subgroup of order p, call it H.
The roots of a primitive polynomial all have order p 1.
The maximal class of a group of order p is n - 1.
A uniform presentation of the extra special groups of order p can be given as follows.
The groups F above have order p 1.
Let - the Galois field of order p the characteristic.
Since groups of order p are always regular groups, it is also a minimal such example.
There are exactly two groups of order p, namely and .