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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?

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