[SOLVED] CS Question 1

Question 1
Security and Networks First Class Test
(a) Consider ElGamal encryption with g = 7, p = 11.
Bob chooses x = 4 as the private key. What is his public key? Show your
workings.
What is the encryption of the message m = 4 with Bobs public key when
choosing rA = 3 as the random? Show your workings. (b) A client established the connection with the server as follows:
[10 marks]
Client and server agree on g and p as used in the Die-Hellman protocol. The client creates a random number x and sends gx mod p to the server. The server creates a random number y and sends gy mod p to the client.
Every message between client and server is encrypted with AES in counter mode using the gxy mod p as the key. In addition the SHA256 hash of each message is sent as well.
(i) Is gxy mod p a good key for client and server? If this is the case, provide a justification. If not, explain why.
(ii) Does this protocol provide authenticated encryption? If this is the case, provide a justification. If not, explain why and provide a remedy. [10 marks]
Question 2
(a) Extracting tar-files changes the owner of the extracted files to be the user who runs the extraction program. Which attack is prevented by this measure? Justify your answer. [10 marks]
(b) ssh refuses to accept public keys for authentication of the user if the .ssh directory is accessible by anyone except the user or the file .ssh/authorized keys2 is not owned by the user or is writeable by others. Assume that firstly, ssh only checks that the file .ssh/authorized keys2 is not writeable by others, secondly that the .ssh-directory for Alice is writeable by everyone and finally that Bob can login into this host. Is it possible for Bob to login into this host as Alice? Justify your answer.
[10 marks]
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Question 3
(a) Consider an openvpn-connection using TLS with forward secrecy for encrypting the trac sent over the VPN. Assume you have access to the private key of the openvpn server and managed to extract a transcript of the encrypted trac over the VPN.
(i) Why can you not decrypt the messages contained in the transcript?
(ii) What would malware running on the openvpn server need to add to the tran- script to make it possible to decrypt the messages contained in the transcript?
Justify your answer.
(b) Consider the following protocol:
A ! B:Epk(B)(NA),A
B ! A:Epk(A)(NA,NB,B)
A ! B : Epk(B)(NB) A ! B : {M}#(NA,NB)
[10 marks]
where NA and NB are nonces, and #(NA,NB) is a symmetric key based on the hash of NA and NB, and pk(A) is the public key of A. Is it possible for the attacker to learn M without knowing any of the private keys of A and B? If so, give an attack in Alice-Bob Notation. If not, explain why. [10 marks]
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