Estimates of Fork-attack effectiveness on blockchain protocol

Abstract

We consider protocol of secure construction and storage of data base, named “blockchain”. This protocol may be considered as some development of control sums and electronic signature schemes on the case when all participants of the set guarantees consistency of the data in the same manner. We construct a formal model of blockchain algorithm. We propose, that so called “long chain condition” is a necessary part of the considered blokchain protocol. We also propose, that when user finds an error, the corresponding block reject with all blocks after it in blockchain tree. For this model we obtained some probability estimates of the events, like error correcting of blocks. We obtain the estimate of mean value of speed of blockchain growth. We demonstrate that modification of these estimates, when some fixed quantity of “adversaries” provide bad blocks may be minimize by “honest” users.  We show that “honest” users may protect against Fork-attack by choosing security parameters, like number of checked blocks in one step. To the other hand in this case, speed of growth of blockchain tree may become negative, and our protocol fall down. We present quantitative bounds.