$(10$ points$)$ Attack on a hash function

Let $E(k,m)$ be a secure $128-$bit block cipher$($you can assume block cipher as $128-$bit AES$).$ We

define a hash function $H(m)$ as follows:

Assume that $|m|$ is multiple of block size i$.$e$.$ padding is not required

break the message $m$ into $n$ blocks like $m=m_0||m_1||m_2||dots|m_{n-1}|$

Apply the following algorithm:

Give a practical collision attack on the above construction of hash function. Here by practical

we mean that the number of message pairs required to be checked for the collision should be

considerably less than the effort required for brute force approach. $($Hint: using birthday attack

find two message $m$ and $m^{\text{'}}$ such that $H(m)=H(m^{\text{'}}).$