The only information requested on the petition, besides your email address, is name and address. That info is available in a wide variety of places on the net. Just google your name and you will find that your address is widely known. Your identity cannot be stolen from signing this petition.
But, just in case you are wary, here are links to Ebay's classified page and cute animals page on facebook:
http://chn.ge/fX5W2S
http://chn.ge/eRb2R9