Clicking one of Haddouche's buttons prompts a file with an "extremely long file name" to download onto the victim's computer once every millisecond. This floods the inter-process communication channel, the processes an operating system uses to respond to user requests. This all causes your browser to become unresponsive, or even crash.
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The attack could even consume so much memory that the OS itself crashes, according to Bleeping Computer, who first reported the story.
Browser Reaper impacts all Firefox versions before 62.0.2, Safari between 9.0 and 12.0, and Chrome 69 and earlier.
There is not yet a known solution to this noted vulnerability. Haddouche has submitted a bug report calling for Firefox to limit downloading multiple files from one site without permission.
While we wait for that to be fixed, there's not a ton you can do to protect against this attack. Just make sure you don't click on sketchy links that you aren't familiar with, as you never know what scripts might be embedded there.