Joined: 09 Oct 2009
Number Nerdery built with fasm
Recently I was explaining big integer crypto to some non-techies, trying to explain to them just how large the numbers are that are used in everyday web commerce, etc. etc ... and discovered it is near impossible to convey it properly without turning them into base 10 and doing some math ... hahah.
Anyway, stuck it here in the heap because it isn't really about programming, though every last bit that composes the page is all written in x86_64 fasm along with using various bits of my library... figured some of you might get a kick out of it.
People are very bad at comprehending large numbers. That's the same reason they can't understand how can a "tiny" cryptographic address be "unique" (with extremely low chance of collision), same reason they don't understand just how much space there is between "objects" in the Universe (stars, planets, etc), etc. I mean, really.
It helps if you give analogies. For example, trivial stuff like:
You know a 32-bit number can represent up to 4GB of unique addressing? Now create a 4GB file. Open it in a hex editor. Appreciate its bytes (literally). It has a lot of bytes right? Try to individually look at the bytes, scroll down or whatever, it seems endless. Each byte is very important so take the time to appreciate its value.
A 64-bit number can address a file uniquely of similar imagined size, but each such byte represents 4GB of data. The entire previous 4GB file now fits in a single "byte" of the 64-bit file. So when you open such a file, and appreciate its bytes, just think each byte is 4GB. Crazy right?
Just imagine how long it would take to just "scan" such a file even at blazing fast speeds (imagine 256GB/s). 256GB/s on a full 64-bit file would take as long as scanning a 4GB file with 256 bytes per sec (most people find the latter extremely slow, it would take you like half a year).
And that's only 64-bit... 128-bit would be the same, but each "byte" in that 64-bit file (meaning, a file whose size is absolutely massive already, even if each byte is a byte) represents an entire 64-bit file!! A 64-bit file may be massive but now each of its bytes is a 64-bit file itself. Wow.
But cryptos use at least 256 bits... now think about that. More intuitive right? Now in such a huge file, imagine you have to find a collision in a byte address (literally, byte) in that file. Sounds like impossible task.
Your page uses way too large numbers though. All I see is just a bunch of digits (hex or not). Maybe try with 256-bits or such?
Joined: 24 Aug 2004
Location: Misner space
Re: Number Nerdery built with fasm
Page works fine without JS. I think I can live without the resampling of the values.
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