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Anon avatar Crypto

How is there a $\frac{1}{poly(n)}$ bias in a multiple-round coin tossing protocol with commitment?

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Anon

On p.2, Example 1.1 (in this paper), there is a description of a coin tossing protocol with bias 1/4. In the paragraph below the example, they note that for a protocol with $r$ rounds (assume for the sake of clarity it is $poly(n)$) there's a bias of $\frac{1}{r}=\frac{1}{poly(n)}$.

I am quite new to Cryptography, and since the paper they cite in this context is quite old and very different to their example, I'm left with two questions:

  1. How can their example (Example 1.1) be adapted to a $poly(n)$ round coin-toss protocol with bias at most $\frac{1}{poly(n)}$?

  2. How is the final outcome in a multi-round coin toss determined? (i.e., we tossed more than one coin each, so what is the final result?)

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