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134. You should really read this-

http://www.eetimes.com/design/embedded-internet-design/4372428/How-secure-is-AES-against-brute-force-attacks-

How secure is AES against brute force attacks?
Mohit Arora, Sr. Systems Engineer & Security Architect, Freescale Semiconductor
5/7/2012 1:29 PM EDT
In the world of embedded and computer security, one of the often debated topics is whether 128-bit symmetric key, used for AES (Advanced Encryption Standard) is computationally secure against brute-force attack. Governments and businesses place a great deal of faith in the belief that AES is so secure that its security key can never be broken, despite some of the inherent flaws in AES.

This article describes the strength of the cryptographic system against brute force attacks with different key sizes and the time it takes to successfully mount a brute force attack factoring future advancements in processing speeds.

Any cryptographic algorithm requires multi-bit key to encrypt the data as shown in Figure 1.







As shown, it will take a maximum 16 rounds to check every possible key combination starting with "0000." Given sufficient time, a brute force attack is capable of cracking any known algorithm.

The following table just shows the possible number of key combinations with respect to key size:






Figure 4: Time to crack Cryptographic Key versus Key size



Faster supercomputer (as per Wikipedia): 10.51 Pentaflops = 10.51 x 1015 Flops [Flops = Floating point operations per second]

No. of Flops required per combination check: 1000 (very optimistic but just assume for now)

No. of combination checks per second = (10.51 x 1015) / 1000 = 10.51 x 1012

No. of seconds in one Year = 365 x 24 x 60 x 60 = 31536000

No. of Years to crack AES with 128-bit Key = (3.4 x 1038) / [(10.51 x 1012) x 31536000]
= (0.323 x 1026)/31536000
= 1.02 x 1018
= 1 billion billion years


As shown above, even with a supercomputer, it would take 1 billion billion years to crack the 128-bit AES key using brute force attack. This is more than the age of the universe (13.75 billion years). If one were to assume that a computing system existed that could recover a DES key in a second, it would still take that same machine approximately 149 trillion years to crack a 128-bit AES key.