A currency can be backed by a trusted issuing authority, by a scarce resource or by the scarcity of its money base (eg bitcoin). Are there any other known working alternatives.
The value of money is derived entirely from others' willingness to accept it in exchange for things of value.
Money has in fact emerged— Rai stones on Yap is the classic example— without the existence of either a "trusted authority" mandating its use (I assume that by "trusted authority" you mean a government-mandated fiat currency) or any recourse to a scare resource (e.g., notes redeemable for silver or gold).
While the Yap stones themselves (the monetary base) were in fact scarce, and some degree of scarcity is a necessary condition for money to act as an effective store of value, it's not a sufficient condition, as FooBar noted in his comment. Even if a monetary base is finite, what matters is that people are willing to accept that form of money as payment, which is in turn generally determined by whether other people will be willing to accept that form of money as payment. It's collective agreement that money has value that makes it valuable. If people some day find no reason to continue using the Rai stones as money (they've been replaced by US dollars for day-to-day use, and they're only used for certain traditional exchanges now), they will lose their value as currency, despite their continued scarcity.
Specifically regarding Bitcoin, there has been significant skepticism in the economics community about whether it is actually a currency, with Yermack (2013) noting that it functions poorly as a store of value and unit of account, and that its transaction volumes have been quite low.