Key management is a particularly difficult problem to solve. Bitcoin solved it using a wordlist, but in this post I argue it didn't solve it well.
Hardware wallets take advantage of how difficult it is to store a 24 or 25 word list securely, and the options users have is either redundancy or reduction of their word list into an access pin tied to the operation and lifespan of an electronic device.
Today, we have alternatives for security neglected in favor of what I assume is money or knowledge-barrier-related. I present one such alternative for technical audiences, along with a script I wrote which does everything described. But until such alternatives become mainstream viable products, non-technical users will have to deal with storing their word lists.
Before we start, let's review what a word list is.
# Word Lists
When you create a new wallet, you're given 25 words from a set of 2048. All these words are from a pre-determined word list called BIP39.
The first and last words from BIP39:
They have a 1:1 representation of your seed (aka the private key).
Convert the first 24 into numbers between 0-2047, and treat it each one as an 11-bit string (2^(11) = 2048). Join all the bitstrings together to create a 32-byte private key (with change). In Algorand, the 25th word is a checksum computed from the first 24.
The 2048 words in that word list represent 2048^(24) states, whereas the private key represents:
256^(32) or 2^(256) or 2048^(23+3/11)
Notice the last exponent comes close to the number of (non-checksum) words provided, but falls short by a fraction. What this means is that the word list contains a bit of extra data in the last word that couldn't possibly fit into the bounds of the 32-byte private key.
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