Pedersen Verifiable Secret Shares (PVSS), Commitments and Spotting A Bad Dealer and a Cheating Player
Okay. Let’s say you are in a card game, how do you know that the dealer is honest, and that the other players are also honest? Well, let’s say we have n players in the card game, and we want to make it fair. For this, we could agree that t players can come together and agree on the card that has been dealt. This would mean that there was a consensus of t people who would approve the card. This would define t as the threshold for approving the card.
For example, we could have Bob, Alice, Carol and Peggy playing the card game, and where Trent is the dealer. If we define that three of the four will agree to the card that is dealt, then we can cope with one cheating player. In this way, Bob, Alice and Carol can agree on a card, even if Peggy disagrees with the card dealt. This is known as Byzantine Fault Tolerance, and where we can cope with players turning bad.
To implement this we can use a Shamir Secret Sharing mechanism to allow at least t players to come together to reveal the card dealt. So first, I will explain the Shamir Sharing mechanism and for us to be able to cope with a…
