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This is a bit of a general question, knowing already of HD wallets and the mnemonic system for creating, backing-up and using the bitcoin blockchain.

However say you have for example a cold/paper wallet, with just one Bitcoin Private Key. Wouldn't an easier way to back-up/save/remember that address be simply be figuring out where the key lies within the range of possible bitcoin keys and taking note of the exponent of said number? Or Additionally a 10 digit scientific notation number, pretty much the same as remembering a phone number...

Example using python:

from bit import Key

# The exact position of this key is 2^65 in int form: 36893488147419103232
privKey = Key.from_int(36893488147419103232)

print(privKey.address)
print(privKey.segwit_address)

This gives the outputs 1LgpDjsqkxF9cTkz3UYSbdTJuvbZ45PKvx and 3FC7umZDWPvTskbVwG7mn72M8RtW8yFSy7. This is so much easier to remember and technically as long as the key was generated randomly enough wouldn't it be just as secure but easier to remember as opposed to 12/24 words one has to write down somewhere, or the hex format or WIF format private key?

After considering other factors... It wouldn't be all that secure if you want to save a key in the range of all possible keys, some exponents of certain numbers produce floats, I assume eventually one would be limited to specific keys, rendering the security bit a quite useless, but I only tested with exponents of 2 my maths could be wrong.

Say the exponent output was always converted to an exponent of the keys position that gives a non-decimal integer, one could in a sense cover all possible keys in the range no? If so then I stand by my question.

I'm trying to understand why this won't work not proving it works.

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Given that private keys need to be random, it's unlikely that a properly chosen private key will be easily represented in the method that you have described. Relying on exponentiation in order to essentially compress the private key will be lossy, or require addition of additional exponentiations. This either leads to reduced security as the private key is no longer uniformly random, or having memorize the entire number anyways, just in a different form.

When it comes to memorization, it's probably easier for people to remember a series of words rather than a sequence of numbers. The words are also able to encode more information per word than per digit in a number, which reduces the number of things actually being memorized. Furthermore, when reading a sequence of numbers, it's easy to lose your spot which can result in memorizing the incorrect number. Lastly, words are also self correcting (with enough letters, the intended word becomes obvious, and BIP 39 is designed such that only the first 3 letters are required), and mnemonics also include a checksum. These make writing down the seed from memory much easier to do.

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  • Ok understood, however, I think I may have been a little all over the place with the question. Again say all I want is to generate a cold wallet, Say I use bitaddress.org's code to securely generate a paper wallet. Then import it using the library I used above, and export it to it's integer wallet format, and I turn the resulting integer into an exponent of whatever number that's exactly equal to the exported integer value. Say its 10^98, that's pretty easy to remember, and I generated securely no?
    – fredsta98
    Dec 16, 2022 at 1:24
  • Please take note I did read through your answer, if you find the time please try look into the Bit library, it may help you better understand my question, it allows for one to have private keys in WIF, HEX, INT, PEM, and DER format. That's pretty much where I got curious...
    – fredsta98
    Dec 16, 2022 at 1:33
  • If given the option for INT, I could simply create a backup of my address into something that's as easy as a number to use maybe I can give a follow up edit to the question to demonstrate how that would work. Again I'm am trying to find the flaws not defend something I'm very sure a lot of people in the bitcoin-core developer team, yourself include have already written off. I really appreciate you taking the time Mr. Chow.
    – fredsta98
    Dec 16, 2022 at 1:34
  • I'm fairly sure that most private keys cannot become a nice exponential that's easy to remember. If you're going to randomly generate keys until you do get one that is a simple exponential, that can still reduce the security of your key since it effectively reduces the search space for your key.
    – Ava Chow
    Dec 16, 2022 at 16:54
  • Alright that makes sense, thank you Mr. Chow
    – fredsta98
    Dec 17, 2022 at 10:24

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