Analysts of the Canadian central bank published a report describing risks of blockchain systems. The research paper calls unrealistic the possibility of 51% attack and double spending.

Bank of Canada specialists modelled the situation when one miner achieves control over more than 50% of the network capacity, using the Proof-of-work algorithm, and is opposed to a group of so-called honest miners. The goal of a malicious miner is to double spend. The report acknowledges that, in theory, a dishonest miner, controlling more than half of processing capacity of the network, can take advantage of this situation, along with such factors as confirming transactions lags, to execute double spending.

"This implies that he is certain to eventually outrun other miners in generating a longer chain and, thus, can always cheat by double spending. However, from an economic point of view, this requires that a dishonest miner has deep pockets and is risk neutral. These assumptions tend to be unrealistic and, in practice, users have little economic incentives to launch such an attack, especially when the computational investment by other miners is large."

According to Canadian experts, for stability and confidence in the blockchain system it is enough to make sure that a 51% attack and double spending will be too expensive for scammers. They also note that there may be several malicious miners, willing to double spend, and it further reduces the risk of successful attack, as they will compete with each other.

"Rather than ruling out double spending altogether, it could be sufficient to ensure that double spending only occurs with a sufficiently small probability. Interestingly, there could then even be competition for double spending where there are multiple dishonest users."

Also, Bank of Canada's experts noted that they consider the Proof-of-Work algorithm to be more reliable and resistant to 51% attacks than its alternative Proof-of-stake algorithm, which, in particular, will be used by Ethereum in the future.

Although the PoS algorithm is more energy efficient, it does not have the key advantage of the PoW algorithm, which requires dishonest miners to make large financial investments to perform a 51% attack. The PoS algorithm is not so reliable from economic point of view and carries more risks that such an attack may be executed.