Modification of RSA Encryption . ( 20 points ) Let p and q be distinct prime numbers and N - p . In the class , to encrypt a message m , We appended...

This question is related to RSA, it is part of a crypto class, if you have any idea how to approach it that would be helpful

3 . Modification of RSA Encryption . ( 20 points ) Let p and q be distinct primenumbers and N - p . q . In the class , to encrypt a message m , We appended a randomstring , to its prefix . We needed to ensure that the resulting number ( / m ) E ZThat is , we need ( m ) to be relatively prime to both p and aIn the class , we used the following trick . We ensured that ( m ) is smaller than bothpand q . This technique ensures that ( m ) is relatively prime to both p and q . Forexample , if pand gare n - bit primes , then we were able to encrypt ( roughly ) ( n / 2 ) - bitmessage musing ( n / 2 ) - bit randomness r . In this problem we shall develop a moreefficient encryption techniqueSuppose N 2 2 2 , Let the message me (0 1 3 / 2 Pick a random r (0 13 + 1 2 . Wewant to argue that the probability of ( m ) being relatively prime to N is very highProve that , for any me ( O , 1 3t / 2 , we have( god ( 1 / m , N ) = 1 1 2 11 5 ( 0 , 13 + / 2( This result shall allow using ( roughly ) ( 3 2 ) - bit messages in with ( 1 2 ) - bit randomness )Solution