A cloaking device is an item gained from one of the native missions. Below is a spoiler 'how to' for users whom do not wish to go about things under the cloak of ignorance.
The device cannot be bought. It is activated by the number 0 above the letters O and P on a standard qwerty keyboard (default settings). It forces your ship to flicker and be removed from radar so people upon whom you fire or even follow haven't the faintest idea you are the culprit. It also allow users to attack GalCop vipers without fear of fugitive rating.
However, the cloaking device slowly ebbs away at your energy banks, therefore rendering it not only temporary, but also a danger if it runs out in the midst of others lasers. (It is your energy banks which allow you to survive post shield failure).
SPOILER ALERT ------- SPOILER ALERT
Highlight this entire space/paragraph to read. The cloaking device mission is informal in the sense you do not get a display screen. On roughly your sixth jump through the 5th galaxy, you shall arrive to meet normally 3 happy vessels. Suddenly, 1 shall fire one you whilst the other just sits there idly. The one that fires on you then turns away - still orange. You could kill them, but better is to wonder where the third ship went? They will start firing on you soon and will flicker visibly, but not on radar. They will be untargetable. Kill them carefully and pick up the cargo. You then have the cloaking device. WARNING - IF YOU MISS THIS MISSION (DEATH, DESTRUCTION OF DEVICE, THEY GOT AWAY) YOU MUST LOAD THE GAME AND TRY AGAIN. THE MISSION DOES NOT COME TWICE!
Repairing the Cloaking Device is not easy. OXP's which help include (i) RepairBots OXP, (ii) Cloak Repair OXP, visiting a Hacker Outpost from the Anarchies OXP, or (iv) visiting the Aquatics Corp HQ in Aqualina and doing them a favour (they might just do you one in return!)