Making The Card Game Honest - For The Players and The Dealer: Meet Feldman Verifiable Secret Shares
Who do we trust on the Internet? Basically, no-one. And so we need to integrate trust into every part of our digital world, as we never know who and what is being dishonest. In a card game, we might have a cheating player, or a player that refuses to show their cards to the other players. But what about a dishonest dealer? How do we detect that?
Well, one way is to share a secret, and then distribute it to the players. The players will then only be able to recover the secret when a given number of them reach a threshold. This can be defined as an any t-from-n scheme. This approach was perfected by Adi Shamir, and who created the Shamir Secret Sharing (SSS) system. But what about a dishonest dealer? How do the entities who receive the shares verify that they are valid? Well one of the best ways was developed by Paul Feldman and is defined as a Verfiable Secret Sharing (VSS) method [1]. One great advantage of this method is that we can use any homomorphic encryption approach [here]:
For this we create a group G using a prime number p and a generator g (typically a value of g=2 or g=5 is…
