I was reading the “Fast Multiparty Threshold ECDSA with Fast Trustless Setup” paper by Gennaro & Goldfeder, 2018 and I encountered this portion (Sect. 2.4, p.6):
This excerpt leaves me slightly confused. First, there’s seemingly a mismatch (a typo?) between r and R — or is it that R is the set from which r is sampled? Second, most important, what are these coin tosses? There’s no mention of coin tosses anywhere else in the paper and after reading some external sources on commitment schemes the only references to coin tosses are in sample applications of commitment, e.g., in an async coin toss scenario.
To summarize, what are these coin tosses and what is R?