Is it meaningful to allow parties to use a non-uniform random tape in 2-party computation? Consider a trivial example where two semi-honest parties want to flip a biased coin. Since the sender is semi-honest, the sender can locally flip a biased coin and send it to the receiver. A natural question is: What does the sender's random tape look like in the above trivial real protocol?
I know that, in the 2-party computation literature, the random tape is assumed to be uniformly random. I am curious about the convention of such an assumption. Is it a mandatory requirement? Many thanks for your comments.
Most models I've come across have a truly random tape. You can use this trick - assume the tape to be uniformly random, but then the party reads a block (of certain size) of random bits and uses that to bias the coin.
For example, if you want the coin to output Heads by probability 0.75, read 2 random bits from the random tape and if they both are 1's, output Heads otherwise output Tails.