ExBin is a pastebin clone written in Elixir/Phoenix. You can find the source code here on github.
None of the pastes are listed anywhere publicly. If you create a paste it will be only visible for the people you show the link to. Each link is generated with a horesebatterystaple kind of identifier, so it’s not impossible to guess an identifier.
Pastes are stored indefinitely. This might change in the future, though. ExBin is still new.