Sender S broadcasts messages to n receivers ?1……………??. Privacy is not important but message authenticity is. Each of the receivers wants to be assured that the messages he has received were sent by S....

Sender S broadcasts messages to n receivers ?1……………??. Privacy is not important but message authenticity is. Each of the receivers wants to be assured that the messages he has received were sent by S. The subjects decide to use a MAC.
1.Suppose all subjects share a secret key k. Sender S adds the MAC to every message he sends using k and each receiver verifies it. Explain why this scheme is insecure.2.Suppose sender S has a set A = {?1 … … . . ?? } of m secret keys. Each receiver ?? has some subset Ai C A of the keys. Before sending a message, S computes MAC Cj of the message for each key fa. Then S sends all MACs ?1 … … , ??with the message. When receiver ? ?receives a message, he accepts it as authentic if and only if all MACs corresponding to keys in ??are valid. Which property should sets?1, … … . . ??satisfy to be resistant to the attack from (1). Assume that the receivers cannot collude. 3.Suppose that n = 6. Show that it is sufficient for the sender to append 4 MACs to every message to satisfy the condition derived in (2). Describe sets ?1, … … . . , ?6 ⊆ {?1, … … . , ?4}.

Extracted text: Sender S broadcasts messages to n receivers R1 Rn. Privacy is not important but message authenticity is. Each of the receivers wants to be assured that the messages he has received were sent by S. The subjects decide to use a MAC. 1. Suppose all subjects share a secret key k. Sender S adds the MAC to every message he sends using k and each receiver verifies it. Explain why this scheme is insecure. 2. Suppose sender S has a set A = {k ... ... km } of m secret keys. Each receiverR; has some subset Ai CA of the keys. Before sending a message, S computes MAC Cj of the message for each key fa. Then S sends all MACS C, ... , Cmwith the message. When receiver Rreceives a message, he accepts it as authentic if and only if all MACS corresponding to keys in A;are valid. Which property should sets A1, . A,satisfy to be resistant to the attack from (1). Assume that the receivers ... ..... cannot collude. 3. Suppose that n = 6. Show that it is sufficient for the sender to append 4 MACS to every message to satisfy the condition derived in (2). Describe sets A1, .., A,C {k1, .., k4}. ..... ...