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recaptcha used to be open source and now it was part of google systems in effort to speed up and fix digitizing problems with books. it was now being served as a service and controlled via API calls to google just like the other google services. i used recaptcha twice and never used it on persoal sites that i created, i use homemade scripts for them.
there are methods to remove the box and the logo below the image all with an API theming call.
ah sorry I can't help you then. I've never used reCaptcha, I just don't feel like it fits in with the aesthetics of my sites. Plus I always prefer using my own stuff so I know exactly what's going on with it.
I don't think it is open source but every time a CAPTCHA gets solved it helps to digitize New York Times archives. And it's really easy to implement as well.
It's the temporary site for my freelance web development and luckily the only free script i've made available for download is an image verification script with very simple to follow instructions for implementing it.
Securimage is an open-source free PHP CAPTCHA script for generating complex images and CAPTCHA codes to protect forms from spam and abuse. It can be easily added into existing forms on your website to provide protection from spam bots. It can run on most any webserver as long as you have PHP installed, and GD support within PHP. Securimage does everything from generating the CAPTCHA images to validating the typed code. Audible codes can be streamed to the browser with Flash for the vision impaired.
They also provide a quickstart guide and live example sites.
An easy way to do capatcha is to ask a simple but logical question like, "What is 2 + 2". or "What letter comes after B?". Then lets say the you choes the 2 + 2 question, you were using post, and it's field name is captcha. Use the code to find out if they did it correctly.