Alice picks the two prime numbers p $=31,$ q $=47$ as her secret numbers for an RSA cipher, and publishes the public key N$,$ e with e $=11.$a$.$ What is N$?$b$.$ Bob wishes to send an enciphered kiss to Alice, so decides to transmit the ASCII code for X $(88$ in decimalnotation$)$ using Alices public key cipher. Let C denote the enciphered message.Using the fact that $8811=888\backslash$times $882\backslash$times $88$ compute C$.$c$.$ On receiving Bobs message Alice computes the private key d in order to decipher it$.$ The number f is defined bythelinearcongruence$11$f $1$mod$($p$1)\backslash$times $($q$1).$Computep$1,$q$1$andsolvethecongruencetofind f$.$