OK, specifically the time delayed mesh network I mentioned above. That is a good reason why you would want those properties. Are you planning on having Eric and Tim communicate directly at some point earlier in the process, to exchange identity data, or are you mediating that through a third party also? (I kind of assume you are establishing initial trust directly...)
Given the "sending code" part, it sounds like you will have some reasonably large data to send, even post-compression, so you might consider using that initial identity exchange to share a (sufficiently random, or human supplied) key, and then use that for
HMAC-SHA1, which should have sufficient security. You could probably jump to HMAC-SHA256 instead if you prefer.
I would suggest you generate those cache tables statically, and simply embed them directly as lua code in your addon. Avoids the high startup cost to generate them in return for some reasonably compressible data, and the same runtime memory use.
Anyway, that requires that Eric and Tim communicate directly once, but never again. (You could even automate this through, eg, the wow mail system, to exchange the key if you prefer -- that allows time-separated communication to share the key while retaining the direct communication for key establishment.)
Good luck.
Correct: it wouldn't avoid the risk that there was a subtle leak or something like that. That said, you could likely audit the code and get reasonable confidence about the behaviour -- DSA shouldn't be insanely huge to implement, even accounting for the need to write bignum handling, etc, in lua. So the library should be of a managable size, I would imagine.
The same is true of the HMAC-SHA1 code I link above, of course, though that is not in the scope of wow as such, so is less likely to be able to do anything hostile in the wow context.