I thought of a way to produce trustless card game in a flexible way. One feature that I want is it should be flexible (It should work for any type of card game, though I indeed started it as a solution for mental poker) and scalable (the number of players should not be limited by anything other than the rules of the particular card game). One feature of this scheme is that it uses no private channel for messages between players, everything to be communicated is to be published on a public ledger (e.g. a block chain). I want some confidence about this part.
Do ECDH and the DH on groups of quadratic modulo a safe prime $p = 2q + 1$ with prime $q$ support the property such that given: $a,b,A=a^x,B=b^x$, with $a,b$ generated pseudo-randomly (replace with scalar multiplication in case of ECDH groups), and $A$ and $B$ coming in any order, no polynomial time algorithm should be able tell whether the order is changed or not with probability greater that of a random guess (1/2) by a non negligible amount. This is an absolute key to my design.