8) Having k (a private key) in ECC and the starting point P on the curve, write a simple program (as a pseudocode or any programming language) to efficiently (i.e. in terms of computability) calculate the public key. Again, in your pseudocode or program assume the operation . (in some documents it is shown by +) has been defined so you can simply apply it on two points on the curve. [6 marks]

DO NOT COPY ANSWER FROM OTHER ONES, PLEASE READ THE QUESTION AND ANSWER.

SAME ANSWER HAS BEEN GIVEN FOR 2 DIFFERENT QUESTIONS HERE SO PLEASE READ THE QUESTION AND ANSWER. DO NOT COPY.

BELOW IS ATTACHED PICTURE FOR THE INFORMATION/REST OF THE QUESTION BUT I ONLY NEED ANSWER FOR THE ABOVE QUESTION NUMBER 8.

hen, based on the RSA and ECC answer the following questions: 1) What is the concept of one-way function in cryptography? [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 (N=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 public channel. Assume the encrypted message sent by Alice is 16. Eve 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 (i.e. N=p.q), thus the original message is 35. Check the program and verify her claim? [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%i==0:print("p=",i,"break; 6) Explain how Eve could find the decrypted message using p and q in part (5). RSA algorithm is not strong enough or Bob missed something? [ 4 marks] 7) Write a simple program (as a pseudocode or any programming language) 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 defined so you can simply apply it on two points on the curve. [4 marks] Explain in which circumstances such a program can find the private key. [2 marks]