Was thinking about putting out a trail camera on public land this summer to get some patterning of deer movement. With theft in mind, was thinking about putting a camera in one of the security boxes. Would this be enough of a deterrent to keep someone from stealing it?

There is nothing that will absolutely keep someone from stealing it if they really want to, best you can do is make it difficult as possible, or unlikely as possible.

I put mine in a surplus .50 caliber ammo can with hole(s) cut just large enough for flash/sensor/lens. Velcro holds cam in place. Long shank padlock (where lack slides off shank) locks the opening mechanisim and fairly hefty chain loops through hefty eybolts attached to can (and chain has lock). I have a couple pictures of it that I may put up sometime to give someone an idea of what it looks like. My first cam (homebrew) survived quite a few curious onlookers and a couple playful skirmishs from a bear without a problem.
Also could help if cam is placed far from the beaten path (maybe in thick stuff where people would be less likely to travel)

YOU CAN ALSO MOUNT THEM HIGH LOOKING DOWN....THAT SHOULD HELP SOME

Never thought about putting them up high looking down.

Agree with WVSPORTSMAN. Keep them out of the line of sight.

I've been using trail cams for years and unfortunately have had more than a few stolen. What I can tell you that is on private property, when someone gets there picture taken, they usually come back and steel the camera because they weren't supposed to be there in the first place. On public land, they usually leave it alone because they're not trespassing.

i have mine on public land but 1 is in a lock box and the other is locked to a tree using a cable. all the locking devices do is keep an honest man honest. the way mine are locked up, they would destroy the camera while attempting to get them off the tree.

i keep all of mine on public land. best advice i can give like others have mentioned is to keep it as hidden as possible, if you are thinking about putting it close to roads or areas where you have seen other hunters hunt, i would be weiry...i usually hunt a good distance from roads or where i usually see people..this really helps, although if you put them up now, not many hunters are willing to take the time to scout, so this could be in your benefit.