Cryptocurrency supplement: How secure is 256-bit security
Added 2017-07-08 14:33:34 +0000 UTCHey everyone,
As promised, here is the supplement to yesterday's video. No charge, of course, since this is an add-on to a different main project. I had a lot of fun putting this together, let me know what you think!
Also, I'm going to do a Q&A session, where you can answer questions here: http://3b1b.co/questions. For you, the patrons, I'm of course happy answer any questions anytime, but this will be a time to sit down and actually record some answers.
-Grant
Comments
Would love to see a Cryptocurrency 2.0 on the changes since 2008, the nuances left out and the possible future of Cryptocurrencies/BTC. Merkl Trees, Shnorr Signatures, Segregated Witness, OP codes, Smart Contracts, etc.
2017-07-13 00:35:51 +0000 UTCSensational!
Illuminati Games
2017-07-11 06:37:25 +0000 UTCLove it!
3blue1brown
2017-07-10 15:57:50 +0000 UTCAnother fun image that is frequently used to drive home the magnitude of 2^256 is this one: <a href="https://miguelmoreno.net/wp-content/uploads/2013/05/fYFBsqp.jpg" rel="nofollow noopener" target="_blank">https://miguelmoreno.net/wp-content/uploads/2013/05/fYFBsqp.jpg</a> But it is worth considering certain points, such as RIPEMD-160 addresses only having 160 unique bits of entropy prior to first spend (per best practice), and lack of any rigorous mathematical proof that the combination of hash functions that produce addresses do not leak further entropy anywhere. ;)
Jesse Thompson
2017-07-09 10:38:59 +0000 UTCI want to build a blockchain application to see how this works inside.. Thanks for sharing the video.
2017-07-09 05:31:50 +0000 UTCIf (and I assume this to be true) a cryptographic hash is truly "random", then every hash is independent of whatever hashes you have tried earlier, so you'll (almost always) end up with hash collisions for some hashes, while other hashes will never occur within those 2^256 guesses. It would then follow a geometric distribution, which has an expected average of 2^256 (1/p) guesses.
2017-07-09 01:53:06 +0000 UTCWonderful video -- very cool. One minor fix: If you're randomly guessing, you'll on _average_ find an answer in 2^255 guesses, not 2^256. You have to on average search 50% of the address space. For certainty, of course, you need 100% or 2^256. Saved you one galaxy!
2017-07-08 14:52:08 +0000 UTCI want kilo-google to become an actual measure of computation :) Only problem is, the abbreviation (kg) might be confusing :)
Christopher Burke
2017-07-08 14:50:52 +0000 UTC
