Towards Optimal Implementation of Decentralized Currencies: How to Best Select Probabilities in an Ethereum-Type Proof-of-Stake Protocol

Nowadays, most financial transactions are based on a centralized system, when all the transaction records are stored in a central location. This centralization makes the financial system vulnerable to cyber-attacks. A natural way to make the financial system more robust and less vulnerable is to switch to decentralized currencies. Such a transition will also make financial system more transparent. Historically first currency of this type - bitcoin - use a large amount of electric energy to mine new coins and is, thus, not scalable to the level of financial system as a whole. A more realistic and less energy-consuming scheme is provided by proof-of-stake currencies, where the right to mint a new coin is assigned to a randomly selected user, with probability depending of the user's stake (e.g., his/her number of coins). What probabilities should we choose? In this paper, we find the probability selection that provides the optimal result - optimal in the sense that it is the least inductive to cheating.