1) What is the concept of one-way function in cryptogaphy? [2 marks] Describe the one-way functions which are used in RSA [2 marks] and ECC [2 marks]. 2) Explain how the private and public keys are defined in ECC [4 marks] 3) Compare the RSA with ECC in terms of the key size and encryption strength [4 marks] 4) Bob uses RSA and chooses the pair (Na=713,e=7) as his public key. Using this public key, encrypt the message M=59. Show your work step by-step. [4 marks] 5) Using the public key in part (4), Alice has encrypted a message (we do not know what was the original message), and sends it to Bob through a poblic channel. Assume the encrvpted message sent by Alice is 16. Fve also has the Bob's public key and receives the encrypted message (sent by Alice). Eve claims that using a simple program (as shown in the following) can find the prime numbers p and q which are used by RSA to calculate N (lie. N=pq. thus the original message is 35. Check the program and verify her daim? [2 marks] Show your work step-by-step. What is the output of the program? [2 marks] Explain how she decrypted the message without having Alice's private key? [2 marks] i=2 N=713 while iifN/6i==0: print("p=",i,"q=break; 6) Explain how Eve could find the decrypted message uning p and in part (5). R5. A algorithm is not strong enough or Bob missed something? [4 marks] 7) Write a simple program (as a pseudocode or any programming lanouge) to show how one can use it to try to find the private key in ECC (having two points P and Q. Assume the starting point on the curve is P and the public key is Q which is another point on the curve, additionally, in your pseudocode or program assume the operation " " (in some documents it is shown by " + ) has been defi ed so you can simply apply it on two points on the curve. [4 marks] Explain in which circumst. Kes such a program can find the private key. [2 marks] 8) Having k (a rivate key) in ECC and the starting point P on the curve, write a simple program (as a pseudocod or any programming language) to efficirntly (ive. in terms of computability) calculate the public key. Again, in your pseudocode or program assume the operation =" fin some documents it is shown by " "+") has been defined so you can simply apply it on two points on the curve. [ 6 marks]