Quote from: o_e_l_e_o on November 13, 2022, 07:29:06 AM

Quote from: larry_vw_1955 on November 13, 2022, 03:26:26 AM

give me a pen and paper, i'll write down a string of 1s and 0s of length 256. i bet no one ever came up with that private key before.

Maybe not, but that doesn't mean the string you produce will be random.

it's not like a book where you just take out some sentence from it and hash it. just waiting to be discovered.

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Studies have consistently and repeatedly shown that humans are bad at both generating and perceiving randomness. If you say to pick a number between 1 and 10, 7 is by far the most common.

Asking someone to pick a random number between 1 and 115792089237316195423570985008687907852837564279074904382605163141518161494337 is different than telling them to pick a number in that range that no one else would ever guess. Or be able to find. And if they did, they would lose all their money. They're going to think a bit about it before just blurting out "777777777777777777777777777777".

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If you say to write down a random series of coin flips (which is the same as writing down a binary number), we consistently avoid runs of the same result (HHH/TTT/111/000) since these are perceived as being "less likely".

They are certainly less likely than HH or TT but the thing is, in some random bitcoin private key you're going to see 00000 and 11111 you might even see larger length repeats. So think about that. 000 and 111 will happen alot.

Example (I dont know how this bitcoin private key was generated but I'm sure it was probably done using software, as most of them are):

1011100000111010000010110010011011011000111110111100001001100011101000011110011010101000001111111110101101110100111100110011010101001000011010000110100001011011110101010010000100 1100000101100110000100100111000110100010010111110111011010111011010001001100

So obviously one needs to understand a little about what is the norm. Then go from there.

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A unique string is not necessarily a random string, nor is a unique string necessarily a secure string. I could generate a brain wallet using the first line of text from a Shakespearean play which had never been used before. My brain wallet might be unique, but any coins I deposit on it would likely be stolen.

But there's a difference. your unique string has been published so that anyone in the world can get a copy of it. mine wouldn't have since I just generated it out of my head.

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Because, humans aren't random number generators. What is randomness? Complete lack of determinism. If something can be accurately predicted, it's not random. A cryptographically secure random number generator comes with more unknown variables to predict, in comparison with a human brain.

If humans did not behave randomly (and unpredictably) then the stock market would be a science. Even with bitcoin, no one knows what the price is going to do. Why is that? because we don't know what people are going to do. their behavior is random. completely random. some of them buy, some sell. the overall result of that is anyone's guess.

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Begin writing. What's the first binary value, and why? You might think there isn't a reason you chose 0 (e.g.) but there is quite likely a reason you don't know.

Well I wouldn't be able to tell you "why". There is no justification of why. it is just what I wanted it to be. At the particular moment in time. Just like all the remaining 255 bits. There doesn't have to be a reason why. There is no way to say why. With that said, I have actually done this procedure of writing down a private key but in hex not binary. I would be confident enough to use it. Enough said. Grin