Comparison of efficiency of Double Spend Attack for blockchains with checkpoints and without them

Abstract

Though Proof-of-Stake (PoS) protocol is widely-used in blockchains, but the first strictly proved results about its security against Double Spend Attack (DSA) were recently obtained. To reduce the probability of this attack, some blockchains use some additional instrument, which is called checkpoints. In this paper, we present explicit formulas for the estimates of probability of success of Double Spend Attack in the case of the Proof of Stake protocol consensus with checkpoints and compare obtained results with probability of classic Double Spend Attack. The formulas obtained allow to get corresponding numerical results, which we compared with the analogical numerical results obtained earlier for "classical" PoS protocol in blockchain without checkpoints. As it was expected, this comparison shows that blockchain with checkpoints, under the same conditions, is more secure against such attack.