Q3) You are helping to design an encryption algorithm. The decryption phase of the algorithm takes two inputs, a message of length digits and a key made up of binary bits. The decryption phase performs a mathematical process on the message using the key to produce the plain text decoded message. You are very

aware that there are hackers that 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, when 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? [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? [5 marks]

(c) The security of the encryption process depends on the value . The decryption process is quite complex. Assume it takes 1 minute of processing time on a PC to apply a key (regardless of the value of ) to the message (regardless of whether its the correct key). The algorithm may be regarded as sufficiently secure provided that, using a brute force method, there is no more than a 1% chance that the message would be decoded correctly in 30 days (working 24 hours a day). Calculate the minimum number of bits that the key must be composed of. [10 marks] (d) In reality, the time it takes to apply the key depends on the value of . If the key is short, the application time is quick. If the key is long, it takes longer to apply. Assume that the time to apply the key to the message is given by the formula = 0.5 where is the number of bits in the key and 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 0.5% chance that the message would be decoded correctly in 30 days (working 24 hours a day). Calculate the minimum number of bits that the key must be composed of.