In this question, we examine some high-level considerations in connection with the security of communications. In a brute force attack, an intruder tries all the possible keys. Assume that the system uses a 64-bit encryption key.

1. How many combinations can be obtained from this system?
2. Assume that the system has a fast processor that tries one key every billionth of a second. Calculate the average time that an intruder needs to crack the code. Assume that the average time will be half of the maximum time. Give the answer in the

nearest billion.

3. Assume that the computing power of the processors increases by a double every year. Complete the following table accordingly starting from the current year (found from part (b) above). (20 marks)

Date	Hours	Days	Years
Year 0 (Current year)
+1
+2
+3
+4
+5
+6
+7
+8
+9
+10
+11
+12
+13
+14
+15
+16
+17

4. Comment on the results found in part (c) above.
5. If the system applies parallel processing using: 4 processing elements, 16 processing elements, and so on. Complete the table below by calculating the average time taken

to crack the code starting from the current year.

Processing Elements	Year 0 (min)	Year 1 (min)	Year 2 (min)	Year 3 (min)	Year 4 (min)	Year 5 (min)	Year 6 (min)
1
4
16
64
256
1024
4096
16384
65536