As others have said, it's some type of scale insect. A telltale sign is that they are mostly arranged on the middle line of the leaves, where, I imagine, it's easiest to hook into the plant's nutrients.
First thing to do is get it as far away as possible from any other plants you hold dear. Until it's sorted out, avoid cross contamination via your hands and tools as well. After that, you'll have to find some type of poison to kill them. Scales can be very resistant to external methods, something that is delivered via the plant's juices that they feed on might be easiest. Or you could spend weeks diligently rubbing the leaves and stems with alcohol to rid of them, to possibly no avail.
(I am not very fond of scales.)