These examples will follow the same step numbers shown in the specifications.

Note: The values used in this example are extremely small to be able to do easy calculations and have small graphs.

Encryption

1.
Ok, lets say we want to encrypt the byte 0b01001000 (ASCII letter "H").
First we will convert it to a point.
In this example, we convert H to (2,-1).

2.
For this 2-Dimensional example, three points are needed to act as key points.
Here, we have generated the points K_{1}=(5,1), K_{2}=(-4,3), and K_{3}=(-6,-2).

3.
The process of encrypting the data is simply calculating the distance between each key point and data point.
In our example, we calculate: K_{1}H=3.61, K_{2}H=7.21, and K_{3}H=8.06.
Therefore the "encrypted" letter H is: 3.61,7.21,8.06.

Decryption

4.
First the key points are set (could be from password or "key file" that was generated and used to encrypt).
The encrypted data is then applied to each key point in the form of a radius:
RK_{1}=3.61, RK_{2}=7.21, RK_{3}=8.06

5. The intersecting point(s) between each circle is found:
I_{K1K2}=(2,-1),
I^{'}_{K1K2}=(3.129,4.082),
I_{K2K3}=(2,-1),
I^{'}_{K2K3}=(-11.103,4.241),
I_{K3K1}=(2,-1),
I^{'}_{K3K1}=(1.4,1.2)

6.
In our example, the intersection point that occurs the most is (2,1).
Looking the point up in our table, the original byte is 0b01001000.