Question

Imagine an attacker has amassed 42% of the network's hash power, and is looking to trick someone by double spending a 3-confirmation transaction.

He sends 10btc to the recipient, recipient waits for 3 confirmations, and sends the attacker some other cryptocurrency in exchange.

Now the attacker creates an alternative transaction that spends the same bitcoins to himself instead, and has to create a block containing his double-spend transaction, as well as more blocks on top of that first one, in order to create a 'longest chain' containing his double spend.

What is his probability of succeeding? Enter answer in percents, accurate to two decimal places.

Answer 1

Answer: PROBABILITY OF SUCCEEDING IS APPROXIMATELY 1.75%

Here we are given that the attacker has amassed 42% of the network's hash power,
thus probability P(massing block chain's mining power) = 0.42

Further, we are given that the attacker sends 10btc to the recipient who waits for 3 confirmations. Now, based on the other given conditions of the problem, we have

n = number of confirmed blocks the merchant requires before releasing goods to buyers = 12

X = Number of progress by blocks while attacker is waiting for the goods

X, here, thus, will be a binomial ( n=12, P=0.2) with probability mass function as follows (refer to the image attached below)

THUS, PROBABILITY OF SUCCEEDING IS APPROXIMATELY 1.75%