What Happens When The Dealer Leaves The Game: Can We Continue? Meet AVSS
Let’s say we have a deal in a card game, and where there are a number of participants (n). For every card dealt, we could split the value of the card into a number of shares, and where a given number of these shares can be brought together to reveal the value of the card. This support Byzantine fault tolerance, and where a number of the parties can fail to reveal their shares. This might be because they do not respond in time, or are cheating players. But what happens when the dealer leave the game? Can we still reconstruct the card? Well, we can with an Asynchronous Verifiable Secret Sharing (AVSS) method.
Outline
In 2002, Cachin et. al defined the Asynchronous Verifiable Secret Sharing (AVSS) method and which uses bi-variate polynomials [1]. In most secret sharing schemes we have a polynomial with one variable, such as:
With Shamir’s Secret Shares we store the secret share at a_0, and where we distribute points on the polynomial and then rebuild them back into a polynomial, and which should then reveal the secret. With AVSS we use bi-variate polynomials and which has two variables (x and y). Bi-variate polynomials are in the form of:
In this case, the secret is kept at a_00. With the Shamir method, we define a threshold (t) from a number…
