a) For a fast encryption in RSA it is popular to use e = 3. Although RSA is considered to be a…

a) For a fast encryption in RSA it is popular to use e = 3. Although RSA is considered to be a secure public-key cryptosystem, the implementations of RSA can made encryption completely insecure. Assume that M ? Z2 64 is a 64 bit plaintext that is encrypted using a 512 bit RSA modulus n and encryption exponent e = 3. Explain why this is completely insecure. Demonstrate this by finding the pliantext corresponding to the ciphertext C = 33076161 when n = 100082119. b) Suppose an active adversary wishes to decrypt a particular message c = me mod n intended for A. Assume also that A will decrypt arbitrary ciphertext for adversary other than c itself. Describe how the adversary can make A to reveal the plaintext message m corresponding to c