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Message Authentication Code is a hashing algorithm where both sender and receiver share a symmetric key . This is a security risk. Which of the

Message Authentication Code is a hashing algorithm where both sender and receiver share a symmetric key. This is a security risk. Which of the following approaches achieves the same goal without having a shared key?
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Encrypt the hash with the senders public key
Sign the hash with the receivers private key
Sign the hash with the senders private key
Encrypt the hash with the receivers public key

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