$1.$ In this problem you will work with the six$-$bit analog of the ve$-$bit

block chain hash function introduced in our Module $7$ lecture notes

$($recall that this utilizes the Matyas$-$Meyer$-$Oseas construction$).$

Using the same function g as described there, along with the initial

value H$0=010110,$ nd the hash value of the message

x $=011100010111011100$

showing all steps and details as we did in our lecture notes.

$2.$ Repeat problem $1,$ but using the Miyaguchi$-$Preneel construction

$($see page $306$ of our text$)$ rather than Matyas$-$Meyer$-$Oseas.