Simplified Entropy: Humanized
1 bit of entropy = 2 possible outcomes
2 bits = 4
3 bits = 8
4 bits =16 etc
The issue with large numbers, like a raw 64 hex BTC private key might look like this:
(e9873d79c6d87dc0fb6a5778633389f4453213303da61f20bd67fc233aa33262)
I think an easier way to grasp this is instead of thinking numbers, think playing cards
A standard 52 card deck (52!) that has been shuffled at least 25 times, has ~ 225 bits of entropy
Imaging shuffling a deck, dealing one by one, and then creating a string of 52 entries
2 Hearts
4 Clubs
7 Spades
King Diamonds
2H4C7SKD etc (104 characters, but 52 entries) this is something we could look at an understand, we could read this.
I like this because you can show me your string, and I call tell you exactly what happened, and know each can only happen once.
Q) How long would it take the world's top 500 supercomputers to construct every single deck composition?
A) 1.7 x 10^29 times the age of the universe. It is highly improbably that there have ever been two shuffled decks with identical final composition in human history, nor will there ever be.
So what would a ~40bit entropy deck look like? ie Mk3 auto generated entropy bug estimates I've seen.
Remove all the 2-9 cards, leaving only A,K,Q,J of each suit (16 cards)
A single maxed out Mac Studio with external storage could probably do this locally in 2-3 days ish. An array of machines could be hours.
Before the cypherpunks point out logical discrepancies, rounding and estimates, this was meant to "humanize" bits of entropy, in something analogue, that makes more sense than 100 dice rolls. IMO
Take a deck of cards, shuffle them, write them down in order, and know that sequence never has, nor ever will happen again. If nothing else, it's a fun party fact.
My sincere condolences to all impacted by the CC entropy bug. No one deserved this.