Post by Ferenan

All the discussion around the recent cold-wallet hack and poor entropy has reminded me just how absurdly large 2²⁵⁶ really is.

A comparison I’ve always liked: the number of possible ways to shuffle a standard deck of cards is 52! ≈ 8 × 10⁶⁷. That’s about 226 bits of entropy. SHA-256 has 256 bits, making its full space about 1.4 billion times larger even than 52!.

But just how large is 52!, Surely there can't be that many ways to shuffle a single deck of cards.... Well,

Imagine starting a timer with 52! seconds on it. Take one step around the Earth’s equator every BILLIION years. Just one step per billion years. Each time you finally complete a lap around the entire world, remove one single drop of water from the Pacific Ocean and set it aside. Then start the whole process again, one step per billion years, one drop removed everytime you go around the world.

Now, when the Pacific is empty, refill it and place a single sheet of paper on the ground. Repeat the entire process, walking, draining the Pacific drop by drop, then adding another sheet of paper, until the stack of paper reaches the Sun.

Now do that whole thing another 1,000 times.

You’ve still only used roughly a third of the timer. We just can't comprehend numbers this big.