Q4)
You are helping to design an encryption algorithm: The decryption phase of the algorithm takes two inputs - a message of length a digits and a key made up of n binary bits. The decryption phase performs a mathematical process on the message using the key to produce the plaintext decoded message. You are very aware that there are hackers who would wish to be able to decode your messages. However, the workings of the algorithm have been kept secret, so the only hack available for decoding the message is a brute force approach where each possible key is tried one at a time until the correct one is found, and a decoded message in English is produced. There are no known cribs, weaknesses, or other techniques to assist in hacking the cipher.
(a) What is the running time for a brute force method to decode a message? Fill the blanks in the answer sheet: [5 marks]
(b) Should the lower bound you identified in part (a) concern us in terms of the safety and security of our encryption technique? Fill the blanks and check the correct boxes in the answer sheet: [5 marks]
(c) The security of the encryption process depends on the value n. The decryption process is quite complex. Assume it takes 20 seconds of processing time on a PC to apply a key (regardless of n and a values) to the message (regardless of whether it's the correct key). The algorithm may be regarded as sufficiently secure provided that, using a brute force method, there is no more than a % chance that the message would be decoded correctly in 30 days (working 24 hours a day). Fill the blanks in the answer sheet and calculate the minimum number of bits n that the key must be composed of. [10 marks]
(d) In reality, the time it takes to apply the key depends on the lengths of n and a. If the key is short, the application time is quick. If the key is long, it takes longer to apply. We discover that the time to apply the key to the message is given by the formula t = 0.01a X n^2, where n is the number of bits in the key, a is the length of the message, and t is the time in seconds. This time, the algorithm may be regarded as sufficiently secure provided that, using a brute force method, there is no more than a 0.25% chance that the message of 200 characters would be decoded correctly in 30 days (working 24 hours a day). Fill the blanks in the answer sheet and determine the minimum number of bits n that the key must be composed of. [10 marks]