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In a $\text{RSA cryptosystem}$, a participant uses two prime numbers $7$ and $11$  to generate public and private keys. If the public key is $13$, then the private key is ____

1. $32$
2. $33$
3. $34$
4. $37$

Given: p=7 q=11

Public key = 13

n=p*q=77

$\Phi$ (n)=(p-1)*(q-1)=6*10=60

Let private key be e

13*e mod $\Phi$ (n)=1

13*e mod 60=1

Therefore e=37 Option (D)
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