Question

DES uses a 56-bit key. Let's say you encrypt a message using single DES. With a 56-bit key there are 2^56 possible different keys. On average an attacker would only need to try half this number of keys to guess the correct key and break the system. If a cryptanalyst can try 1,000,000 keys per second, how long on average would it take to discover the key and recover the plaintext?

Answer 1

So there are a total of 2⁵⁶ different keys out of which half will be tried
Which means that a total of 2⁵⁵ will be tested.

So in one second, we can test 1 000 000 keys
We need to find this in terms of
2^x = 1000000
log₂2^x = log₂1000000
x = 19.93

So 1000000 = 2²⁰

We need to open 2⁵⁵ patterns
each second can try 2^19.93 patterns
Total Time = 2⁵⁵ / 2^19.93
= 2^{55 - 19.93}
  = 2 ^35.67 Seconds = 36067990609.81 Seconds

And this time is close to greater than 1100 years thus one would not be able to open this encryption.

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