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Task 6. Various Questions (2 marks) Answer the following questions. You do not need to implement any program for these tasks. These tasks are pen-and-paper exercises. Please show all your workings for Task 6.1 to 6.4. Answers without showing the workings receive no mark. 1. Assume that the size of the message space (domain) for a given hash function is 25. Also, assume that we want the chance of the adversary finding a collision to be at most 2^-30. What is the size of the hash (in bits) required? (0.5 marks) 2. Sign and verify the message m = 11 using the RSA signature when p = 59, q = 47, and e = 15. (0.5 marks) 3. Demonstrate that the RSA signature with the parameters given in Q2 is forgeable under chosen message attack with two messages m = 2 and m = 3. (0.5 marks) 4. Adam and Bob share the same modulus n = 21 for RSA, and encryption exponents e = 5 and e = 4 with gcd(e, Ï†(n)) = 1. Charlie sends them the same message m encrypted with e and e respectively, resulting in the ciphertexts ca = 14 and co = 7. Eve intercepts both ca and co and applies a common modulus attack to recover the message m. What is the message m? (0.5 marks) In order to obtain full marks, submit Task6.pdf together with the other tasks in this assignment to Moodle.

          Task 6. Various Questions (2 marks)

Answer the following questions. You do not need to implement any program for these tasks. These tasks are pen-and-paper exercises. Please show all your workings for Task 6.1 to 6.4. Answers without showing the workings receive no mark.

1. Assume that the size of the message space (domain) for a given hash function is 25. Also, assume that we want the chance of the adversary finding a collision to be at most 2^-30. What is the size of the hash (in bits) required? (0.5 marks)

2. Sign and verify the message m = 11 using the RSA signature when p = 59, q = 47, and e = 15. (0.5 marks)

3. Demonstrate that the RSA signature with the parameters given in Q2 is forgeable under chosen message attack with two messages m = 2 and m = 3. (0.5 marks)

4. Adam and Bob share the same modulus n = 21 for RSA, and encryption exponents e = 5 and e = 4 with gcd(e, Ï†(n)) = 1. Charlie sends them the same message m encrypted with e and e respectively, resulting in the ciphertexts ca = 14 and co = 7. Eve intercepts both ca and co and applies a common modulus attack to recover the message m. What is the message m? (0.5 marks)

In order to obtain full marks, submit Task6.pdf together with the other tasks in this assignment to Moodle.

6task 6various questions2 marks answer the following questions you do not need to implement any program for these tasks these tasks are pen and paper exercises please show all your workings 69387

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