A cryptography problem on breaking AES

[ecy5maa]

3. Suppose the NSA (National Security Agency of the US) has a specialized computer system that can break a DES cipher by brute force search in 1 minutes on the average. Estimate the length of time the same system will take to break an AES cipher of key length 192 bits by brute force, assuming that the amount of time the system takes to try an AES key and a DES key are the same. Express the answer I terms of the number of years and also in terms of the earth’s age (assume earth age is 4.5 billion years).

 

(Note that in cryptographic calculations such as these estimates, exact numbers are not necessary. Rather the orders of magnitude should suffice.)

 

 

Ans: So what I get is....56x10^31 years and in terms of the current age of the earth: 56x10^25.

 

 

Can some please check....this is using a DES with a 56 bit key.