Question $1$

$[13]$

a$)$ Timestamps and nonces are some of vital tools for network security..

i$.$ Briefly explain a nonce and its role in network security.

ii$.$ Under what circumstance would you prefer to use a nonce over a timestamp?

iii. Kerberos employs both nonces and timestamps. Explain why timestamps $($not only nonces$)[2]$ required in Kerberos.

b$)$ Public announcements is one of ways in which public keys could be distributed.

i$.$ Give one weakness of this approach.

ii$.$ One improvement of the public announcement is the use of a publicly available directory.

Explain why directories as well do not quite work.

c$)$ Give and briefly explain any two applications of cryptographic hash functions. Also provide an

example cryptographic hash algorithm.

d$)$ With aid of a diagram, show how hash functions $($using public key cryptosystems$)$ can be used to

provide a digital signature.

Question $2$

$[22]$

a$)$ Suppose Alice and Bob wish to do Diffie$-$Hellman key exchange. Alice and Bob have agreed upon a prime $\backslash ($ p$=13\backslash ),$ and a generator $\backslash (\backslash$mathrm$\{$g$\}=2\backslash ).$ Alice has chosen her private exponent to be $\backslash (\backslash$mathrm$\{$a$\}=5\backslash ),$ while Bob has chosen his private exponent to be $\backslash ($ b$=4$ a $\backslash )$

i$.$ Calculate all public key components for both Alice and Bob, as well as the final $($shared$)$ secret that Diffie$-$Hellman produces.

ii$.$ Diffie$-$Hellman is susceptible to man$-$in$-$the$-$middle attack. Briefly explain how an adversary could instigate this attack. Also explain how this attagk could be thwarted.

b$)$ Using ElGamal cryptosystem, show the signature that Alice will send to Bob given; $\backslash ($ q$=17\backslash ),$ a primitive root $\backslash (\backslash$bmod $\backslash$mathrm$\{$q$\}=7\backslash ),$ and private key exponent $\backslash (=11\backslash ).$ Also assume Alice selected K as $5$ and message hash $\backslash (\backslash$mathrm$\{$m$\}=12\backslash ).$

c$)$ Suppose your RSA modulus is $\backslash ($ n$=5\backslash$times $11\backslash )$ and your encryption exponent $\backslash (\backslash$mathrm$\{$e$\}=3\backslash )$

i$.$ Find the decryption exponent $\backslash ($ d $\backslash ).$

ii$.$ Assuming that $\backslash (\backslash$operatorname$\{$gcd$\}($n$,$ m$)=1\backslash ).$ Show that if $\backslash ($ c $\backslash$equiv m$^\{3\}(\backslash$bmod $55)\backslash )$ is the ciphertext, then the plaintext is $\backslash ($ m $\backslash$equiv c$^\{$d$\}(\backslash$bmod $55)\backslash )$

Question $3$

$[17]$

a$)$ A simple key distribution scheme shown below in which Public$-$Key Encryption is used to establish a session key.

A

As$-$

$-(1)$ E$($PUb $,[$N $1||$ IDA $])$

A$.-(3)$ E$($PUb$,$ N$2)$

A

$(4)$ E$($PUb$,$ E$($PRa $,$ Ks $))-$

$\backslash ($ c$\_\{1\}=$q$^\{$k$\}\backslash$bmod q $\backslash )$