Problem 9
In what way does a hash provide a better message integrity check than a checksum (such as the Internet checksum)?
Problem 9
In this problem, we explore the Diffie-Hellman (DH) public-key encryption algorithm, which allows two entities to agree on a shared key. The DH algorithm makes use of a large prime number p and another large number g less than p. Both p and g are made public (so that an attacker would know them). In DH, Alice and Bob each independently choose secret keys, SA and SB, respectively. Alice then computes her public key, TA, by raising g to SA and then taking mod p. Bob similarly computes his own public key TB by raising g to SB and then taking mod p. Alice and Bob then exchange their public keys over the Internet. Alice then calculates the shared secret key S by raising TB to SA and then taking mod p. Similarly, Bob calculates the shared key S´ by raising TA to SB and then taking mod p. a. Prove that, in general, Alice and Bob obtain the same symmetric key, that is, prove S = S´. b. With p = 11 and g = 2, suppose Alice and Bob choose private keys SA = 5 and SB = 12, respectively. Calculate Alice’s and Bob’s public keys, TA and TB . Show all work. c. Following up on part (b), now calculate S as the shared symmetric key. Show all work. d. Provide a timing diagram that shows how Diffie-Hellman can be attacked by a man-in-the-middle. The timing diagram should have three vertical lines, one for Alice, one for Bob, and one for the attacker Trudy
Problem 10
Suppose Alice wants to communicate with Bob using symmetric key cryptography using a session key KS. In Section 8.2, we learned how public-key cryptography can be used to distribute the session key from Alice to Bob. In this problem, we explore how the session key can be distributed—without public key cryptography—using a key distribution center (KDC). The KDC is a server that shares a unique secret symmetric key with each registered user. For Alice and Bob, denote these keys by KA-KDC and KB-KDC. Design a scheme that uses the KDC to distribute KS to Alice and Bob. Your scheme should use three messages to distribute the session key: a message from Alice to the KDC; a message from the KDC to Alice; and finally a message from Alice to Bob. The first message is KA-KDC (A, B). Using the notation, KA-KDC, KB-KDC, S, A, and B answer the following questions. a. What is the second message? b. What is the third message?
Problem 10
Can you “decrypt” a hash of a message to get the original message? Explain your answer
Problem 12
What does it mean for a signed document to be verifiable and non-forgeable?
Problem 13
In what way does the public-key encrypted message hash provide a better digital signature than the public-key encrypted message?
Problem 13
In the BitTorrent P2P file distribution protocol (see Chapter 2), the seed breaks the file into blocks, and the peers redistribute the blocks to each other. Without any protection, an attacker can easily wreak havoc in a torrent by masquerading as a benevolent peer and sending bogus blocks to a small subset of peers in the torrent. These unsuspecting peers then redistribute the bogus blocks to other peers, which in turn redistribute the bogus blocks to even more peers. Thus, it is critical for BitTorrent to have a mechanism that allows a peer to verify the integrity of a block, so that it doesn’t redistribute bogus blocks. Assume that when a peer joins a torrent, it initially gets a .torrent file from a fully trusted source. Describe a simple scheme that allows peers to verify the integrity of blocks.
Problem 14
The OSPF routing protocol uses a MAC rather than digital signatures to provide message integrity. Why do you think a MAC was chosen over digital signatures?
Problem 16
What is the purpose of a nonce in an end-point authentication protocol?
Problem 18
Is the message integrity scheme based on HMAC susceptible to playback attacks? If so, how can a nonce be incorporated into the scheme to remove this susceptibility?
