Asynchronous Agreement for Weak Coin from Graded BCA Sample Clauses

Asynchronous Agreement for Weak Coin from Graded BCA. The framework presented in Algorithm 1 relies heavily on the common coin giving the same random value to each non-faulty party in a given round. If the coin were to sometimes give different values to different parties, Lemma 3.4 would no longer hold, which could lead to agreement breaking. − + − ⊥ − More concretely, the following bad scenario could occur: a non-faulty party 𝑥 decides value 𝑣 in its BCA in a round 𝑟 , and gets 𝑣 from its coin in round 𝑟 as well, and therefore commits 𝑣. However, all other non-faulty processes decide in their BCA in round 𝑟 and receive a coin value of 1 𝑣. In this case, it is possible that these non-faulty parties decide 1 𝑣 in the BCA of round 𝑟 1, and could potentially commit 1 𝑣 if their coin for round +
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