Well that kinda sucks! You have to be moving like a quantum bat out of multidimensional hell just to get 2 Earth days for every one of yours - looks like around .8c or so - which sort of defeats the whole purpose. I don't think I can pretend we have ships that can do .99c in a ScientiFiction-y type story. It would need to be pure fantasy.
Well, there is the hidden ultra-fast computer under the surface of the moon. A string of processors lies a mere 30 meters below the surface of the moon, encircling the whole moon. These processors were accelerated to close to the speed of light, using technology that makes CERN's LHC look like the work of children.
Information can be programmed into the processors at various points, as the processors whip around at .999999762c. I could get into more details, but I have a roof to patch.
The point is this: 2^16 bit encryption takes a certain amount of time to crack: one must send the information to Alice at the Moon, who sends it to one of the Bobs (there are many Bobs encircling the Moon) to crack, who then sends it back to Alice, who sends it to Ralph on Earth. There is sometimes a backlog, but generally one can crack a 2^16 bit key in under 8 minutes.
Keep that in mind when you believe your communications are secure. They are, unless Ralph sends them to the Moon.