How do private and public keys work together in cryptocurrency transactions?

@mandy 

In cryptocurrency transactions, private and public keys work together to provide a secure and efficient way to transfer funds. Here's how they work:

1. Public Key: A public key is a cryptographic code, which serves as the receiver's address or the destination address for a cryptocurrency transaction. It can be shared openly with others without any security risk.
2. Private Key: A private key is a secret code that is known only to the owner and is used to access and control the funds associated with the corresponding public key. It must be kept secure and should never be shared with anyone.
3. Generating a Transaction: When a user initiates a cryptocurrency transaction, they create a digital signature using their private key. This ensures the authenticity of the transaction and verifies that it was initiated by the rightful owner of the funds.
4. Transaction Verification: After creating the digital signature, the transaction, including the sender's public key and the digital signature, is broadcasted to the network. Nodes in the network validate the transaction's digital signature by using the sender's public key, ensuring it matches and is indeed signed by the corresponding private key.
5. Confirmation and Recording: Once the transaction is verified and confirmed by nodes in the network, it becomes a part of a block in the blockchain. The blockchain is a decentralized ledger that maintains a complete and transparent history of all cryptocurrency transactions.
6. Public Key as Recipient Address: When someone wants to send funds to another individual, they use the recipient's public key as the address. This ensures that only the person possessing the corresponding private key can access and use the funds received.

Overall, private keys are used to secure and authorize transactions, while public keys are used to generate addresses for receiving funds. Together, they establish ownership, authenticity, and confidentiality in cryptocurrency transactions.

@mandy 

Additionally, private and public keys are mathematically related, specifically through cryptographic algorithms. The private key is randomly generated and used to create a digital signature, which is unique to each transaction. On the other hand, the public key is derived from the private key using a mathematical process.

When a transaction is broadcasted to the network, the digital signature and the public key are included. Nodes on the network can then use the public key to verify the authenticity of the digital signature. By applying the same cryptographic algorithm, they can confirm that the transaction was indeed signed by the corresponding private key without needing to know the private key itself. This ensures that only the owner of the private key can create valid transactions.

Furthermore, public keys are also used to encrypt information that is intended for the receiver's eyes only. For example, when someone wants to send a message or encrypted data to a specific individual, they can use the recipient's public key to encrypt the information. This ensures that only the person with the corresponding private key can decrypt and access the message.

In summary, private and public keys work together to provide secure transactions in cryptocurrencies by allowing the creation of digital signatures, verifying authenticity, and encrypting sensitive information.