what are 1s private key 2s private key 3s private in this BTCWP img

[cafter]

q.1. https://ibb.co/44040Gc
in this 2nd point satoshi talks about signatures ,
please anyone can tell me what is meaning of this 2nd point , in simple words, it's very confusing to understand for me .

q.2 . What are signatures that we use to verify the transaction and what is PGP signatures,at many places i seen that, begin pgp signatire- end pgp signature,
 is there is something hidden in pgp signatures?

[pooya87]

in this 2nd point satoshi talks about signatures ,
please anyone can tell me what is meaning of this 2nd point , in simple words, it's very confusing to understand for me .

In simple terms this is what you do whenever you send a transaction. You create a transaction by entering the receiver's address (that is created using their public key) and then use your private key in your wallet to "sign" that transaction. The receiver will do the same when they want to spend those coins and that creates a "chain".

q.2 . What are signatures that we use to verify the transaction

Bitcoin uses ECDSA and ECSDSA for its signature algorithms and they are found in all transactions you send using your private keys.

and what is PGP signatures,at many places i seen that, begin pgp signatire- end pgp signature,

PGP is an encryption and signing algorithm that used for encrypting messages (in Emails, files, etc.) and for creating signatures which you would mostly see when you want to verify the authenticity of a file (like a wallet's binaries).

[digaran]

Forget about technicality, first grasp the concept.

Block chain(central bank).
Nodes(bank's branches).
Private key(you).
Public key(bank account).
Signature(your signature when opening account and transferring).
Public key cryptography has extra features/functions.

I send money to your bank account(public key) only you can spend the money.
Now replace money with a message, I send(sign) a message with your public key, only you can read it because you(are) have the private key.
PGP, is a close source application, GPG is not, regarding bitcoin they are irrelevant.
Picture you posted is a technical explanation to show how we can replace banks safely where everyone could make sure about the legitimacy and authenticity of transactions.

[odolvlobo]

I thought I understood how a signature works, but I guess I don't. Sorry. I'm glad there are people here who can correct and clear up my misunderstandings.

[pooya87]

In general, a signature consists of a public key

Signature does not contain the public key. The signature scripts in bitcoin transactions usually come with a public key.

and a hash of the message that has been encrypted with the private key.

There is no encryption being done in message signing.
Encryption is the process where you create a "cipher text" which can then be decrypted using the private key to get the original message. However, in a signing operation we should already know the message and the verification is done using the public key.
The operations are called signing and verification not encrypt/decrypt.

The public key is used to decrypt the hash,

As I explained. Also in any decryption algorithm you use the private key to not the public key to decrypt.

[garlonicon]

It proves that the message is associated with the owner of the private key.

It doesn't have to. It is possible to create a valid signature, where the private key will remain unknown. For example:

Code:

message="Hello World"
address="1psPJZYEJrjPtY6kw5Tqtj4mW2yXSSDuH"
signature="GwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAE="

Because nobody knows the k-value that gives R-value of 020000000000000000000000000000000000000000000000000000000000000001, the private key remains unknown. Note that it is possible only for cases, where key recovery can be used, so it cannot be applied to Taproot.

Signature does not contain public key.

I would argue that R-value of the signature is always a valid public key. Of course, it should be different than the public key connected with that signature, because if d=k, then it can be easily calculated by anyone.