Suppose that Alice encrypted a message with a secure cipher that uses a 40-bit k

Question

Suppose that Alice encrypted a message with a secure cipher that uses a 40-bit key. Trudy knows the ciphertext and Trudy knows the algorithm, but she does not know the plaintext or the key. Trudy plans to do an exhaustive search attack, that is, she will try each possible key until she finds the correct key. a) How many keys, on average, must Trudy try before she finds the correct one? b) How will Trudy know when she has found the correct key? Note that there are too many solutions for Trudy to manually examing each one - she must have some automated approach to determining whether a putative key is correct or not. c) How much work is your automated test in part b) ? d) How many false alarms do you expect from your test in part b)? That is, how often will an incorrect key produce a putative decrypt that will pass your test?

Explanation / Answer

a) To determine the correct one key Trudy must try 239 number of keys , Because the given key space is 240 , When divided by 2 , 240/ 2 = 239 possible keys are to tried by Trudy on an average .

b) To count the number of words that message contains Trudy must scan the message , which can done by using computer and a text file with dictionary words. In the process the keys which return largest number of words are the best keys to approach.

c) The automated work to find the key is heavy of resource , The message should be scanned many times repeatedly to find a word from dictionary , It takes so much of time and requires many resources to complete the task.

d) There can be many false alarms from the test , because everytime when some amount of words found are threshold it will show as that possible key is found. A message can be made by using many words from many keys but it is not necessarily to be correct and can decrypt a different message.

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