摘要：We consider the problem of amplifying two-party coin-tossing protocols: given a protocol where it is possible to bias the common output by at most Ï, we aim to obtain a new protocol where the output can be biased by at most Ï* < Ï. We rule out the existence of a natural type of amplifiers called oblivious amplifiers for every Ï* < Ï. Such amplifiers ignore the way that the underlying Ï-bias protocol works and can only invoke an oracle that provides Ï-bias bits. We provide two proofs of this impossibility. The first is by a reduction to the impossibility of deterministic randomness extraction from Santha-Vazirani sources. The second is a direct proof that is more general and also rules outs certain types of asymmetric amplification. In addition, it gives yet another proof for the Santha-Vazirani impossibility.
