This is related to https://crypto.stackexchange.com/questions/48622/how-safe-is-xor-with-multiple-independent-but-non-random-keys but not exactly the same question.
Let's say there are three different vendors in the market, they sell a product called preprinted key tag. A preprinted key tag is a stainless steel card engraving with a barcode encoding a 256 bits random number. It is solid, waterproof, and fireproof, safe to store for a long time. In other words, a preprinted key tag is a random number in cold storage.
I don't trust the vendors, they might secretly keep a copy of those random numbers they sell. I don't trust the independence of the vendors, they might collude together. I don't trust any retail seller, they might secretly steal the information before they sell the preprinted key to me. I don't trust any delivery company, they might secretly steal the information before they pass the preprinted key to me.
The only guarantee is, those random numbers printed on the stainless steel cards are as random as from any modern crypto-secure random number generator, no matter from which vendor.
Now, here is what I am going to do:
- Buy my first preprinted key tag from Vendor A via online shopping.
- Buy my second preprinted key tag from Vendor B via a local retailer.
- Travel to another country, buy my third preprinted key tag from Vendor C via a retailer in that country, and come back to my country.
Finally, XOR the above three 256 bit numbers from these three tags to create a private key. Then lock those three preprinted key tags in a vault. In case someday I forgot the private key I can recover it from the three tags in my vault.
Assume the last step is safe, in other words, assume my vault is safe.
My question is: how safe is the private key created in this way?