Hello, I\'m having trouble finding the formulas or explanation of how to do the

Question

Hello, I'm having trouble finding the formulas or explanation of how to do the following problem:

There is an encrypted message with a secure cipher that uses a 40bit key.The attacker knows the ciphertext and the algorithm. The attacker does an exauhstive search attack.

a) How many keys on average must Trudy try before she finds the correct one? (I found 2^39 but it's based on a formula I found but I'm not sure its the right one)

b)How will the attacker know when they have found hte correct key? Note that there are too many solutions for the attacker to manually examine each one-- she must have some autoamted approach to determining whether a putative key is correct or not. (I would say by validating each one but I'm not sure if that's what they mean by an automated approach...I feel like there should be a formula of some sort.)

c)How much work is your automated test in part b? (if it is validating each one I would say constant time. But again that depends on whether or not I answered b correctly)

d) How many false alarms do you expect from your test in part b?

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.


Thanks , let me know if there is any concern.

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