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  • Paloju Vasudev thinks this is interesting:

ifferent each time, but created from the same private key

From

Cover of Mastering Bitcoin, 2nd Edition

Note

Mathematics, my boy.

You combine the private key + transaction data, and use some mathematics to create a digital signature.
You can then take the digital signature + transaction data + public key, do some more mathematics with them, and the result will confirm whether a legitimate private key was used to create the digital signature.

Because remember, the goal of a digital signature is to prove that you’re the owner of a public key.