Here's a breakdown of how your information is used and/or collected by Stay on the Line (bottom line: we try to be pretty good about these kind of things).
Information We Collect
Stay on the Line does not store any information on your device.
Information You Share
There is no option to share any user data through the game. You can always let your friends know that Stay on the Line is an awesome game though!
Stay on the Line does not store anything that would require any kind of security.