Running this command seems to be a reliable way to produce a pubkey from a valid private key that for Bitcoin. Is this a correct assumption?
openssl ec -inform DER -text -noout -in <(cat <(echo -n "302e0201010420") <(echo -n "PRIVATE_KEY_HEX_STRING") <(echo -n "a00706052b8104000a") | xxd -r -p) 2>/dev/null | tail -6 | head -5 | sed 's/[ :]//g' | tr -d '\n' && echo
These magic values:
Openssl seems to use these values for DER encoding rules, and it doesn't seem to have anything to do with secp256k1 or Bitcoin specifically. Is this a correct assumption?
It doesn't seem like the y^2 = x^3 + 7 formula / secp256k1 is used anywhere explicitly when deriving the pubkey from the private key in the above openssl command.
Are all public keys for Elliptical Cryptography practically derived the same way.. meaning there is a ton of overlap between these ECDSA curves?
Seems like the only thing specific to Bitcoin compared to another ECDSA curve is the maximum upper limit for a private key of
FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141.. is this a correct assumption? How is it that I'm able to produce the private and public keys without having to use the formula? It's like Satoshi lied to us and this formula has no meaning!
A bit confused here would love if someone could clear this up for me and the 2 other people who can't sleep at night because of this.