I doubt it's more complicated than knowing the language and having the proper transmission hardware. 1978 seems a little early to be worrying about hacks of that variety. That said the hardware could also have some kind of encryption built in. I'll ask if I get a chance, though - I hope to get some details from the project soon.
> Arecibo is the only thing big enough right now.
Not entirely true. How did they control it in the 1970's?
They chose Aricebo because it allows them to use very low power antennas to communicate. The size of the dish makes up for the lower power transmission.
In the past, they used high-powered antenna arrays.
Very true. Keep in mind, though, higher power is more expensive.
They've said in the past (I'm failing to find the reference right now) that they chose Arecibo because of the high-gain of the antenna. I believe that the amplifiers that they're actually using above the dish are somewhere around 700 Watts.
Antennas with large effective apertures (of which Arecibo's is the largest) are considered high gain antennas, which have small angular beam widths. Friis' Transmission Equation shows that you could use low-power transmitters, but still maintain high boresight with a sufficiently large antenna surface. :)