Probability of Double Spend Attack for PoS Consensus with Ouroboros Praos Slot Leader Election Procedure

The paper obtains upper estimates for the probability of a double spend attack on Proof-of- Stake consensus with Ouroboros Praos protocol for slot leader election. In compare with simplified models of PoS consensus, considered before in [2], we investigate two models (named Model 1 and Model 2), taking into account all features of Ouroboros Praos protocol [1]: slot creation function, active slot coefficient, possibility of empty slots and slots with multiple slot leaders (both honest and malicious), non-linear dependence between stake ratio and probability to become slot leader in some timeslot, end even non-zero synchronization time (for Model 2), measured in timeslots. In Model 1 (with zero synchronization time), we obtain explicit formulas for the exact double spend attack probability value. In Model 2 (with non-zero synchronization time), we have to make some simplification assumption in favor of the adversary. As a result, we get an upper probability estimation, using so-called dominated distribution.