So, the attacker has X% of the hashrate. The attacker is trying to mine 16 blocks in the time that the honest miners mine at most 15 blocks, because e.g. the victim waits for 15 confirmations on transactions of the attacker’s deposit amount. If the honest miners get fewer than fifteen blocks, the attacker still wins at the 16th, they can just wait for the fifteenth block (or even help mine it, to add to their alibi).
Kindly, Satoshi Nakamoto left us a formula that addresses exactly this scenario in the whitepaper on page seven:
Source: Bitcoin Whitepaper
Even with a hashrate of 30%, the chance of success for such reorganization lengths is pretty low. Satoshi calculated further:
q=0.3
z=0 P=1.0000000
z=5 P=0.1773523
z=10 P=0.0416605
z=15 P=0.0101008
z=20 P=0.0024804
Which gives one percent chance of success with thirty percent hashrate to displace 15 blocks.
Obviously, the chance would be higher if the attacker could leverage more than 30%, but even 30% seem fairly unlikely, given that this would require at least two, more likely three of the largest hashrate providers to make themselves available for such an attack, or even more of the smaller ones.
via miningpoolstats.stream/bitcoin
Further, general computing power is useless, since Bitcoin uses specialized hardware, and there is hardly any SHA-256 hashrate rentable. Crypto51, a website dedicated to tracking the cost of a majority attack for various networks, estimates that a majority attack on Bitcoin would cost about $1.2 M per hour at the going rate for hashpower, but the rentable SHA-256 hashrate via Nicehash only amounts 34% of BCH’s hashrate, which itself is a fraction of 1% of Bitcoin’s hashrate.
via crypto51.app
So, unless the attacker manages to take control of multiple existing mining pools for multiple hours, this doesn’t really seem particularly feasible.
