Not really related to the article, but ever since I learned that homomorphic encryption exists I wondered if it is possible to make a trustless internet poker g

Not really related to the article, but ever since I learned that homomorphic encryption exists I wondered if it is possible to make a trustless internet poker game. That would entail some type of homomorphic encryption where each party would get to know which cards they drew, but not anyone elses. The type of system I am imagining has each player generate a permutation of 52 cards, encrypt it with their key and then take everyone's encrypted permutations together and decrypt a result where they only get to see the 5 cards they got dealt. Is there any research into multi-key systems or ways to apply a single key system to get the kind of result I am looking for?