What key element is necessary for a sender to verify their identity and ensure message integrity in communication?

To ensure that a sender can verify their identity and maintain the integrity of a message, the sender's private key is essential. In public key cryptography, each participant has a pair of cryptographic keys: a public key and a private key. The private key is kept secret and is used to create digital signatures for messages the sender wants to send.

When the sender uses their private key to sign a message, they are essentially attaching a unique cryptographic fingerprint to that message. This signature serves a dual purpose: it confirms that the message was indeed sent by that specific sender, as only they possess the corresponding private key, and it ensures that the message has not been altered during transmission. Any modification to the message would invalidate the signature, thereby signaling any tampering and ensuring message integrity.

The other options involve keys that either don’t serve the function needed for the sender's verification or are related to the recipient rather than the sender’s own identity. For example, the recipient's public key is used for encrypting messages intended for the recipient, while their private key is crucial for decrypting those messages, but does not play a role in the sender’s ability to sign or authenticate their own messages.