Such a cryptocurrency would need to include:

• Support for at least 10^22 nodes.

• A peer-to-peer protocol that accounts for delays in communication up to thousands of years long. (Including seemingly inconsistent delays caused by relativity of simultaneity.)

• A hashing algorithm that's robust to attacks by a network of planet-sized quantum computers.

• Mining incentives that can last for at least 10^14 years. (Or whatever other verification method is being used. You'd probably want to avoid proof-of-work so as not to waste such massive amounts of negentropy.)

Along with anything else I haven't thought of.