Securing Transactions

Describe the Diffie$-$Hellman algorithm. $(3$ marks$)$

Consider a Diffie$-$Hellman scheme with a common prime $q=11$ and a primitive root of $=2.(3$ marks$)$

a$.$ Show that $2$ is a primitive root of $11.$

b$.$ If user A has public key $Y_A=10,$ what is A$\text{'}$s private key $x_A?$

c$.$ If user $B$ has public key $Y_B=7,$ what is the secret key $K$ shared with $A?$

In the Diffie$-$Hellman key exchange, each participant selects a secret number $x$ and sends the other participant $a^x$ mod $q$ for some public number

What would happen if the participants sent each other $x^a$ for some public number a instead? Can Eve break the system without finding the secret

numbers? Can Eve find the secret numbers? $(3$ marks$)$

Describe three security requirements of a cryptographic hash function. $(3$ marks$)$

What is a "brute$-$force" attack on a hash function? Describe two types of brute$-$force attacks. $(3$ marks$)$

Suppose $H(m)$ is a collision$-$resistant hash function that maps a message of arbitrary bit length into an $n-$bit hash value. Is it true that, for all

messages $x,x^{\text{'}}$ with $x{x}^{\text{'}},$ we have $H(x)H(x^{\text{'}})?$ Explain your answer. $(3$ marks$)$

Describe three properties of a digital signature. $(3$ marks$)$

SSH is organized as three protocols that operate on top of TCP$.$ Describe these three SSH protocols. $(3$ marks$)$

What is the difference between transport mode and tunnel mode? Which mode is typically used to secure a VPN connection? $(3$ marks$)$

What is a replay attack? Describe the role of the sequence number field in a replay attack? $(3$ marks$)$

Describe the Transport Layer Security $($TLS$)$ service in detail. Why is there a separate Change Cipher Spec Protocol, rather than including a

change$\_$cipher$\_$spec message as part of the Handshake Protocol? $(5$ marks$)$

What is the difference between a TLS connection and TLS session? $(5$ marks$)$

What is IP Security $($IPsec$)?$ Provide four examples of the use of IPsec. $(5$ marks$)$

In what order should the signature function and the confidentiality function be applied to a message? Explain your answer. $(5$ marks$)$

What is a Security Association $($SA$)?$ What parameters identify an SA$?(5$ marks$)$