Show that if p = 11, q = 5, x = 3, and k = 3, then (x k (mod q) and (x k (mod p) are different. alice and bob want to exchange encrypted signed messages. alice’s public key is (n, e) and private decryption exponent d, whereas bob’s public key is (n0 , e0 ) and private decryption exponent d 0 .

alice wants to send a message x to bob. she first signs a message encrypted by bob’s public key so sends y = (x e 0 (mod n0 ))d (mod n) to bob.

to read the message and verify the signature, bob computes z = y e (mod n) = x e 0 (mod n0 ) and then computes z d 0 (mod n0 ) = x e 0 d 0 (mod n0 ) = x.

will this work? explain why or why not.

Write a car class having two private member variables called tank and speed. write public methods called pumpgas and gofast. the method pumpgas gets an integer for gas that must be pumped. that value needs to be added to tank (no more than 20 gallons). it must return the amount of gas that is purchased ($4 per gallon). the method gofast should increase the speed by 5 each time it is called.write a constructor for the above class that initialized both variables to zero.write a tostring to display both the tank and speed when the car is printed.modify the car class to implement the interface comparable and an interface called carinter having the public methods in carinter.write the main program to create an array of size 5 of type car. create 5 car objects having each location of the array to refer to one of the cars. test the pumpgas, gofast, equals method on the array items. write an enhanced loop to print all the car values (using a tostring written last time).write a generic method to find the minimum of four items. pass int, double, char, string and car objects to test this method.