Permissions: Some background information regarding the permissions that this extension uses and why: These permissions are quite extensive and technically allow this extension to see whatever data your browser sends or receives. (Hopefully the code reviews that Modzilla performs prevent any published extension from abusing those kind of permissions. Still, I would always completely disable any extension that has this kind of permissions while I am using sensitive applications like telebanking, (etc) and preferably only enable it when I actually need it!)

<all_urls> The extension's logic is not limited to certain domains (since it has no advance knowledge regarding which sites might or might not be hosting videos).
webRequest & webRequestBlocking These permissions are needed to intercept the requests made by the original web page and to issue the same kind of requests to then download the video streams: While the extension is "turned on" the video detection logic scans all the loaded files in search of video stream information (which may come in the form of HLS playlists, JSON based configurations or embedded HTML/JavaScript code). The actual files are scanned since request/response meta information may be deceiving.
tabs & activeTab In order to give meaningful names to downloaded video streams, the extension accesses the active browser tab - e.g. to use the page's title (etc).
storage Only used to store the extension's user settings locally (e.g. to keep the extension "turned off" until the user turns it back on).
downloads Used to store a completely downloaded video in the local file system via the browser's standard download mechanism. (The extension doesn't care about the user's download history and uses none of the respective APIs.)

Geliştiricinin yanıtı