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1.
A Trojan is a program which infects a computer and allows a hacker to gain entry by one form or another.
A Backdoor Trojan is one which allows sets up some kind of server service on the computer for hackers to channel data through

It is also a slang term for a gay person who likes to give another gay person a big one up the bum
Example 1
Straight IT worker: Hey theres some kind of trojan affecting the server. I hope its not a Backdoor Trojan.

Gay IT worker: OOh I wouldnt mind it, as long as its a big one.
Example 2
Gay guy: Oooh you know that guy we met last night, ooh he turned out to be a Backdoor Trojan, yes, he was at the backdoor trying to screw my data out all night long. I can hardly walk
by Edgar Allen Post September 22, 2006
 
2.
The sexual act of hitting it doggy style then pulling out and ramming it in the back door.
Dude remember that slut I met at the club? Totally pulled a back door trojan on her. Don't think she will add me on Facebook now.
by DasCracka January 25, 2011