Explain how digital signatures contribute to the security of end-to-end encrypted communication and describe the mechanism used to verify their authenticity.

Digital signatures play a vital role in enhancing the security of end-to-end encrypted (E2EE) communication by providing authentication and integrity assurance. They ensure that the message originates from the claimed sender and that the message has not been tampered with during transit. While E2EE primarily focuses on confidentiality through encryption, digital signatures address the equally important aspects of authenticity and integrity.

In the context of E2EE, digital signatures are particularly important in the key exchange process and also for message integrity verification. During key exchange, which is necessary to establish the shared secret key used for symmetric encryption, digital signatures help to prevent man-in-the-middle (MitM) attacks by verifying the identity of the communicating parties. If Alice and Bob are communicating using an E2EE protocol such as Signal, during the key exchange each party signs their public key before transmitting it to the other. Without this digital signature process, an attacker, Mallory, could impersonate Alice or Bob and replace their genuine public keys with their own, enabling Mallory to intercept and decrypt all further communications while deceiving Alice and Bob.

To understand how digital signatures contribute to security, let's delve into the mechanism used for their generation and verification. Digital signatures rely on asymmetric key cryptography, where each user possesses a key pair: a private key and a public key. The private key is known only to the owner, and the public key is freely shared with others. To create a digital signature, the sender, for example Alice, first generates a hash of the message they want to sign. This hash is a fixed-size representation of the message, ensuring that any change to the message will produce a different hash. Then, Alice encrypts this hash using her private key. This encrypted hash is the digital signature, and it is appended to the message being sent.

When Bob receives the signed message, he first computes the hash of the message using the same hashing function used by Alice. Then, Bob decrypts the digital signature with Alice's public key. If the message was altered by a third party, the hash of the message would no longer match and so Bob would know not to trust it. Because only Alice could have encrypted the hash with her private key, Bob can also have confidence that the message did indeed come from Alice. If the decrypted hash matches the calculated hash, the signature is considered valid, and two key security properties are guaranteed. First, authentication: Bob is sure that the message came from Alice, as only Alice's private key could have created a valid signature that decrypts with Alice's public key. Second, integrity: Bob knows that the message has not been tampered with during transmission, because if any part of it had been altered, the calculated hash would be different from the decrypted hash.

For example, suppose Alice wants to send Bob an end-to-end encrypted message along with a digital signature using the RSA algorithm which is a popular choice for generating digital signatures. She would first create the message, compute a hash of the message, then encrypts this hash using her RSA private key, appending the encrypted hash to the message as her digital signature. Bob receives the message, and Bob uses the same hashing function to calculate the hash of the message and then decrypts Alice’s signature using her public key. Bob verifies the signature by ensuring that his calculated hash is equivalent to the hash he decrypted with Alice’s public key. If they match, then Bob knows that Alice sent the message and that the message was not modified in transit. This is how digital signatures provide the security in E2EE.

In addition to securing message transmission, digital signatures are crucial for identity verification during the establishment of secure communication channels. For instance, they are commonly used to sign the public keys in the key exchange phase to prevent MitM attacks. If, for example, Alice’s public key is digitally signed with her private key, when Bob receives the key, he can verify that key was generated by Alice by checking the signature with her public key. This guarantees that Bob is exchanging messages with Alice and not an imposter. This key authentication using digital signatures is essential to protect communication channels from MitM attacks.

In summary, digital signatures play a dual role in securing E2EE communication by providing both authentication of the sender and integrity of the message. By leveraging asymmetric key cryptography and secure hashing algorithms, they ensure that communication partners can verify each other's identities and that messages have not been altered, making E2EE systems more robust and reliable. They are essential to establish secure channels by verifying public keys and also to safeguard each message sent across such channels.