Robots are bypassing the easy "blue hedgehog" and etc not questions. I don't have any ideas as to what better system to have however if helpdesk admins had any ideas please add them in the comments.
Also a system that shows what admin verified new accounts. (It's currently a little chaotic)
I'm thinking a CAPCHA-like system. Hear me out, but I'm not sure if PHP is innately capable of something like this.
We need to dynamically generate warped-looking text. Just start with printing a random alphanumeric sequence in the middle of a box. (Don't use common words, otherwise it's liable to a dictionary attack. I think.)
Then warp/fisheye random places. Tint some areas some random colors. Draw a line through it. Warp some more for good measure (if you want).
It's essential that no straight lines are drawn before the first warping operation, otherwise it can possibly be reconstructed through some clever trickery. OCR is powerful as it is, so we ought to be careful.
Then take the answer and check if it matches the original string. Save it server-side so it can't be sniffed.
To save resources, asynchronously load it so the user isn't waiting 10 years for the server to generate this.
Of course, a human should be able to do this after a little thinking. Maybe give them a couple tries before placing them in cooldown or something of the like.
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