Euclidean Distances And Polynomials
Polynomial operations are increasingly used in cryptography as a replacement for matrix operations. This is especially true in lattice encryption. So, let’s look at an example of using polynomials, and apply it to detect the difference between two vectors.
We increasingly have complex datasets, and where we need to find the nearest match of a given set of values. For example, we may have a database of facial points, and where we hold the measurements for a scan of a face. In the following, we see measurements for Billy Connolly’s right pupil, the length of his nose, and the length of his upper lip [here]:
When a new face is being scanned, we will thus go through our database of these features and find the one that matches closest to it. For this, we often use a Euclidean distance to find the closest match.
Euclidian distance
With the Euclidean distance, we measure the distance between two vector points, which is often used to find out the nearest vector to a given point. The Euclidean distance between (6,4,3) and (9,2,1) will thus be:
