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p$=178011905478542266528237562450159990145232156369120674273274450314442865788737020770612695252123463079567156784778466449970650770920727857050009668388144034129745221171818506047231150039301079959358067395348717066319802262019714966524135060945913707594956514672855690606794135837542707371727429551343320695239$

g$=174068207532402095185811980123523436538604490794561350978495831040599953488455823147851597408940950725307797094915759492368300574252438761037084473467180148876118103083043754985190983472601550494691329488083395492313850000361646482644608492304078721818959999056496097769368017749273708962006689187956744210730$

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$(1)$ Implemenent $160-$bit random number geneation and secure hash algorithm SHA$1$;

$(2)$ Use a Crypto Library to implement the modular exploentiation algorithm for larger integers and use your implementation to output y$=$gx$($mod p$),$ where x$=$SHA$1($your student ID$).$

$(3)$ After randomly genetating a and b$,$ output $($A$,$ gA$($mod p$))$ and $($B$,$ gB$($mod p$))$ and the secret key gAB $($mod p$)$ established between your VPC $($named by your first name$)$ and your data centre $($named by your surname$)$ by the Diffie$-$Hellman key exchange protocol, where A$=$SHA$1($a$,$ your first name$)$ and B$=$SHA$1($b$,$ your surname$).$

$(4)$ Can you perform a Man$-$in$-$the$-$Middle Attack to the Diffie$-$Hellman key exchange protocol? If so$,$ show attacking steps.

$(5)$ How does IKEv$2$ overcome the Man$-$in$-$the$-$Middle Attack? Show steps.

Note: Please submit your codes, computation results, security analysis and secure protocol.