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Build an authentication mechanism, which will block account after N tries for a given IP address, from which log in attempt was conducted.
To minimize the possibility of blocking an owner's account we may take under consideration other characteristics like User-Agent or X_FORWARDED_FOR (if it's present).
Moreover, after N login attempts, but before blocking the account, we may include additional verification by comparing data entered by the user and data displayed to him/her on the picture (CAPTCHA).
Such approach should slow down, limit log in attempts only to the valid user or even prevent conducting unwanted attempts generally.