It's quite possible, as long as the cost of the current ASICs out there is less than a billion. You can match the current world rate and secretly mine. It would be a combination of buying your own miners and renting hashrate, but mostly it would be renting. Maybe paying a big mine to do it for you.
When I saw the initial math, they said 40 days. But that doesn't include the fact that as you buy hash power, it's price would go up. But to secretly mine for a week before reorganizing the chain would be very possible with this amount of money.
I wonder if you could put in a checkpoint system. And if that could even be decentralized.
I did some quick math a while ago on the cost to buy 51% [0].
When I did it the network hashrate was 44,000,000 TH/s and if you could buy enough S9i's to the same low price, it would cost you around $650 million. This is excluding any other infrastructure you'd need and of course the power you'd use to perform the attack. And since I did the calculations the hashrate has -doubled-, making it cost quite a bit more than a billion.
Now maybe you can get off cheaper if you try to rent the hashrate. Around $18 million of BTC is mined per day, say you can get 50% for $10 million per day. So yes maybe you can do it for 40 days, if you want to risk a large part of that billion. And face the quite massive risk of tanking Bitcoin's value or facing devs who might launch a "protective hard fork".
(This is assuming you -can- buy or rent enough hashrate, which is very uncertain).
There are checkpoints in BTC, although they haven't been added since 2014.
By the time you could source that many S9is, the hash rate would be higher, requiring you to source more, at which point maybe newer and better chips have come out, raising the hash rate yet again, making your investment worthless.
Buy it wouldn't exactly be a secret if you're paying a big mine to do it, or if you purchased every available mining ASIC out there at once (and found enough electricity/cooling to run them all).
When I saw the initial math, they said 40 days. But that doesn't include the fact that as you buy hash power, it's price would go up. But to secretly mine for a week before reorganizing the chain would be very possible with this amount of money.
I wonder if you could put in a checkpoint system. And if that could even be decentralized.