🚀 go-pugleaf

   RSA's intended system appeared in a paper in the book THE MATHEMATICAL
GARDNER (papers in honor of Martin Gardner).  Subsequently flaws were found
by Lipton and probably others.  One problem is that, even if you can't
recover N from f(N), you may be able to get partial information which could
be useful (I think the specific problem for RSA was whether N was a square).
For more details, see CODES and CRYPTOGRAPHY by Welsh, a book by Salomaa
whose title I can't remember, and probably other places.

   I think playing poker raises problems that go beyond the issues involved
in flipping a coin over the phone, specifically figuring out how to make
sure two people don't get the same card.

   A crude approach for coin flipping:  I announce N = product of two big 
primes.  You try to guess whether the middle digit of the smaller factor
is even or odd.  (this was off the top of my head--- no guarantee it doesn't
have a flaw)

   A system for poker based on Probabilistic Encryption (rather complex,
not straightforward use of PE) was published in FOCS or STOC by Goldwasser
and Micali around 1982.

   A year or so ago, I saw a paper ``How to play any mental game.''  Didn't
read it, but it seemed to involve interactive verification protocols.