> 2. The adversary has unlimited computing power: in this case, you need hardware that can generate truly random bits and can only return randomness at the rate the hardware gives you the bits
What would you need those bits for in that case? Literally the only things that comes to my mind is generating one time pads, as standard cryptography is useless in such scenario.
Game-theoretically, you want a source of random numbers when you need to make a decision your adversary can't predict. Traditionally some cultures have (accidentally?) used bird augury for this, but obviously that won't do when you're up against Unlimited Computing Power, as birds are basically deterministic.
What would you need those bits for in that case? Literally the only things that comes to my mind is generating one time pads, as standard cryptography is useless in such scenario.