Question

Alice and Bob want to establish a secure communication channel between them. They do not care about the confidentiality of the messages being transmitted, but they do want to ensure the integrity and authenticity of the messages. Assume A and B share a common key K. Answering the following questions.

a. How can they achieve their goal only with secret key cryptography?
b. How can they achieve their goal with hash function h and the key?
c. Can they get non-repudiation? If yes, how? If no, why?
d. Describe a way A and B can get non-repudiation. Explain your assumption and draw a diagram to show the procedure.

Answer 1

a. They can achieve their goal of ensuring the integrity and authenticity of messages with secret key cryptography by using a Message Authentication Code (MAC) generated with their shared key K.

b. To achieve their goal with a hash function h and the key, they can use a Hash-based Message Authentication Code (HMAC) where the hash function is applied to the concatenation of the message and the shared key K.

c. No, they cannot achieve non-repudiation solely with secret key cryptography, as this method does not provide evidence that a specific party sent the message.

d. To achieve non-repudiation, A and B can use a digital signature scheme. A signs the message with their private key, and B verifies the signature using A's public key. This ensures that the message came from A, providing non-repudiation.

Step-by-step explanation:

a. In secret key cryptography, a Message Authentication Code (MAC) can be generated by applying a symmetric cryptographic function to the message using the shared key K. This MAC is then sent along with the message. The recipient, who also possesses the key K, can generate a MAC and compare it with the received MAC to verify the integrity and authenticity of the message.

b. Using a hash function h and the key K, a Hash-based Message Authentication Code (HMAC) can be generated. The HMAC involves applying the hash function to the concatenation of the message and the shared key K. This approach ensures that only those with knowledge of the key can verify the integrity and authenticity of the message.

c. Non-repudiation, the assurance that the sender of a message cannot deny having sent the message, cannot be achieved solely with secret key cryptography. This is because both parties share the same key, and therefore, the sender could deny sending the message, claiming that the other party generated the MAC or HMAC.

d. To achieve non-repudiation, A and B can employ a digital signature scheme. A signs the message with their private key, and B verifies the signature using A's public key. This cryptographic process ensures that the message originated from A, and A cannot later deny sending the message, providing non-repudiation.