I don't think that you can tackle this problem in Laravel (nor plain PHP) at all. The filtering should be done through DNS with a service such as Sucuri, Incapsula or CloudFlare or on server side. Maybe this serverfault thread can give you some clues.
Mar 27, 2016
4
Level 1
how to avoid empty session id flood
attackers keep posting with empty sid header, server would keep generating new session storage and soon will be flood how should we handle this in L5?
I looked around and it seems that there is no easy way to prevent session and cookie from writing
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