https://vitalik.ca/general/2019/05/12/fft.html
Ctrl+F for "binary fields".
753 karma · joined December 31, 2012
https://vitalik.ca/general/2019/05/12/fft.html
Ctrl+F for "binary fields".
Definitely some kind of weird dynamic going on...
"224" is actually a really nice object to recognize because it's 7 * 32, and if you can recognize other multiples of 32 it frequently gives you shortcuts. It's less useful for addition because you would need to get lucky and get a multiple of 32 (or 7) on both sides, but for multiplication and division it helps a lot.
2. Once smart contract wallets properly gain adoption, you'll be able to do recovery (see: https://vitalik.ca/general/2021/01/11/recovery.html )
3. Lots of built-in anti-sybil techniques (eg. verifying that the address has nonzero balance is a pretty simple and effective one)
Like... why _not_ dump Merkle roots on-chain?
My own experience with thinkpads has been one of non-stop frustration with battery life. The T495 advertises something like 14h of battery life; the actual battery life I got running stock Ubuntu on it was.... less than 3 hours, and that's with power optimization packages that do things like making USB no longer work installed. I recently switched to a system76, and so far its battery lasts easily 6-9 hours depending on what I'm doing.
I imagine you would have to talk to the analytics firms to get the best-in-class attempts to figure out what the split between individual users is.
So unless you're measuring the world as a whole, you're measuring communities that have porous relationships with the outside world to some degree or other. But of course, cryptocurrencies are still much more porous than countries are.
This post has nothing to do with assurance contracts (which that paper seems at first glance to be equivalent to). Instead, it's tackling the different problem of what if there is some established mechanism that is already collecting fee revenue, and it wants to do use that revenue to support its wider ecosystem.
https://twitter.com/StatefulWorks/status/1417157834702209031
(This is perhaps what's not clear to readers from outside the crypto space: all of these discussions are assuming that this is being implemented by some project that has network effects and can extract fees that are necessary anyway for congestion-control reasons, where the only remaining question is where those funds go)
See also this piece by me on social recovery (a related but not quite the same concept): https://vitalik.ca/general/2021/01/11/recovery.html
But this is all not quite the same as reversal and makes different tradeoffs.
Applications can be partially decentralized and that's often the best approach, sure.
The good news though is that you don't need permanent storage of history to be supported by the base protocol itself. Consensus nodes don't need to know about history to verify the current chain. There are plenty of other mechanisms for storing historical data: bittorrent, centralized archives, Filecoin-style networks, etc etc. You just need the blockchain's throughput to be not _too_ high, so that it's actually possible for these protocols to store what comes out.
Definitely nothing is permanent, but you can get pretty close to "permanent unless civilization collapses", and that's much better than "data could drop at any time if a few people just forget"!
This is not how the Ethereum PoS chain's LMD GHOST fork choice works. If >1/3 drop offline, you stop finalizing, but the chain keeps growing.
(Keep in mind that in present-day Ethereum, the influence that PoW miners have in protocol governance is pretty minimal)
Hacking billions of dollars of cryptocurrency is NOT easy, and it gets harder with every passing month, because validators and hodlers have billions of dollars of incentive to protect themselves.
As far as I can tell, the power held by miners has been minimal; if miners had any significant power at all then the various issuance reductions and now EIP 1559 would not have been accepted nearly so smoothly. So when miners are replaced by PoS validators, the power that PoS validators will be inheriting is not that much...
> Yes there will be a number of custodians "competing" with each other, but they will all largely operate under the same regulatory jurisdiction (or at least cooperating jurisdictions)
Even if this is true (given all the decentralized staking pools coming out, and the still really large number of solo stakers, I really doubt it!), I don't see how that state of affairs would survive any attempt by governments to actually use their jurisdictional power. It's very easy to move stake around (or at least it will be very easy post-merge), so once a single pool does anything disagreeable people can just move their ETH to other pools. And staking infrastructure can live in any country; there aren't even constraints around needing to have cheap electricity there.
> This is external to the system and can be done without paying off any existing Bitcoin actor
I've heard this argument many times, but.... why does that even matter? Making a PoW farm requires paying off a hardware provider. Hardware providers are far more centralized than cryptocurrency hodlers, of which there are millions and you just need to find one willing to sell to you. "I want to buy coins but the existing hodlers are all colluding to not let me" is not a problem that anyone in the cryptocurrency space actually worries about in real life. Specialized hardware manufacturers, on the other hand, are few enough that such a thing is at least actually plausible....
(And there's BTC holders with more than 0.3% of all BTC)