3.Consider the brute-force attack. a. Assume the keys used in a cryptosystem are

Question

3.Consider the brute-force attack.

a. Assume the keys used in a cryptosystem are 10 bits long and it needs 1 second to test an individual key by using the brute-force attack. In the worst case, how much time would it take for the attacker to determine a particular key?

b. If the time needed to test an individual key reduces to 0.001 second, how much time would it take now to determine a particular key by using the brute-force attack in the worst case?

c. If we increase the length of the keys to 20 bits and the time needed to test an individual key is still 0.001 second. How much time would it take now to determine a particular key by using the brute-force attack in the worst case?

d. What can you observe from Questions a-c?

Explanation / Answer

In brute-force attack, we consider all the possible ways to determine the right key.

a)

key size is 10bit long

for one individual key it will take 1 second to test

worst case, we have to test all the possible keys with key size.

We have 2^10 keys are possible, in order to find out the right key, in worst case we need to test all the 2^10 keys. For one key to test it takes 1 second. So to find the right key in worst case it takes 1second*2^10. That is 1024 seconds.

b)

Now, the time needed to test one individual key is 0.001 seconds.

And possible keys in worst case are 2^10. (key size is still 10bit long)

So it takes 0.001*2^10. i.e 1.024 seconds

c)

Now the key size is 20bit long.

So the possible keys in worst case are 2^20.

And time taken to test one individual key is 0.001 seconds

So the time taken to determine the right key in worst case is 0.001*2^20.

That is 1048.576 seconds

d)

From questions a to c, we observed that

If time taken to test the key is decrease then time taken to determine the right key in worst case is also decreases when key size is constant.

And also if key size is increases then time taken to determine the right key in worst case is also increases when time taken to rest the key is constant.

The time taken to determine the right key in worst case in brute force attack is depends on the factors of

key size and

Time taken to test individual key

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.