Question $4$

The kid$-$RSA algorithm is a simplified version of the RSA algorithm. Kid$-$RSA

takes as its input four numbers a$,$ b$,$ a$1,$ b$1.$ The four numbers are

converted into four values $M,e,d$ and n $,$ according to the following equations:

$M=a*b-1$

$e=a{1}^{*}M+a$

$d=b1*M+b$

$n=\frac{e*d}{M}$

A plaintext message $P$ can be encrypted to an encrypted message $C$ with

the public key $(n,e)$ using:

$C=e*P(modn).$

Once encrypted, C can be converted back to P using the private key $\text{'}$d$\text{'}$

as follows:

$P=C*d(modn)$

$($a$)$ if $a=949,b=112,a1=524$ and $b1=4266,$ calculate $M,e,d$ and $n.$ Show

your working.

$($b$)$ State the public key for these values of $a,b,a1$ and $b1.$

$($c$)$ Encrypt the message 'Silver' using the public key. Show your working.

$($d$)$ Decrypt the message. Show your working.

$($e$)$ Name a simple shift cipher.

$($f$)$ Explain how the shift cipher you mentioned works, with examples.

$($g$)$ How would you go about cracking a shift cipher.

$($h$)$ Research the enigma encryption that was used in the second world war.

i$.$ What kind of cipher was this?

ii$.$ Compare it to the shift cipher you mentioned above

iii. Which cipher is the most secure$?$ Why?

solve all the parts of this question