I am new to cryptography and would like to understand how a digital signature works between a buyer and a Bitcoin seller. How does transaction authentication between buyer and seller look for? Please explain in more detail here this formula that I found here:
X '= (X + H (X || C) * G)
[with H a hash function, || concatenation, and G the secp256k1 generator point]
How do I understand this formula is the exchange of values between the buyer and the seller? Maybe I'm mistaken about something, but I want to understand if there is an exchange of values, can the sender put additional values in "Transaction" and receive another "Signed transaction" completely different values of "RawTX". Does he violate the signature? A well-known example in the Bitcoin Blockchain. Many senders insert various encrypted values in "OP_RETURN". Can they, with these cunning manipulations, extract the recipient's private key?