QUESTION $3[$Total marks: $20]$ Consider a toy RSA example in which the public key is $($N $=55,$ e $=17).3($a$)[6$ Marks$]$ Determine the value of the private key. $3($b$)[7$ Marks$]$ Describe how a digital signature can be implemented using RSA. Describe a technique which can be used to perform the mathematical operation used in this digital signature more efficiently using the prime factors of the modulus, and use this technique to generate the digital signature for the message digest value $35.3($c$)[7$ Marks$]$ Describe how a digital signature can be verified using RSA. Give an efficient algorithm which can be used to perform both encryption and decryption in RSA, and use this algorithm in the verification of the digital signature value calculated above.