$Q1.$

RSA E$-$Signiture Algorithm

Step $1.$ Key Generation

Person A generates a key and send public key to Person B$.$

Choose two prime numbers $(p$ and $q)$

Compute $n=p^{**}q$

Compute $(n)=(p-1)**(q-1)$

Choose e such that $e(n)d(d^{**}e)mod(n)=1nmcc=m^e$modncBcm$=c^d$modnm,$m=8pq1$ and $e$ and $(n)$ are coprime. $(Their$ greatest common divisor $is1)$

$5.$Compute a value for $d$ such that $(d^{**}e)mod(n)=1$

Public key $is(e,n)$

Private key $is(d,n)$

Step $2.$ Signing

Person A chooses $m$ and computes $c,c=m^e$modn, and sends $cto$ Person $B.$

Step $3.$ Confirmation

Person $B$ confirms whether the messages came from

Person $Aor$ not.

The decryption $of$ ciphertext $cis$

$m=c^d$modn

Using the above$-$explained RSA algorithm, encrypt and decrypt the message $m,m=8,$

Hint: Choose small $p$ and $q$ for easiness.