Notice the exponential increase in possible combinations as the key size increases. "DES" is part of a symmetric cryptographic algorithm with a key size of 56 bits that has been cracked in the past using brute force attack.

There is also a physical argument that a 128-bit symmetric key is computationally secure against brute-force attack. Just consider the following:

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.

There are more interesting examples. The following snippet is a snapshot of one the technical papers from Seagate titled "128-bit versus 256-bit AES encryption" to explain why 128-bit AES is sufficient to meet future needs.

If you assume:

Every person on the planet owns 10 computers.

There are 7 billion people on the planet.

Each of these computers can test 1 billion key combinations per second.

On average, you can crack the key after testing 50% of the possibilities.

Then the earth's population can crack one encryption key in 77,000,000,000,000,000,000,000,000 years!

The bottom line is that if AES could be compromised, the world would come to a standstill. The difference between cracking the AES-128 algorithm and AES-256 algorithm is considered minimal. Whatever breakthrough might crack 128-bit will probably also crack 256-bit.

In the end, AES has never been cracked yet and is safe against any brute force attacks contrary to belief and arguments. However, the key size used for encryption should always be large enough that it could not be cracked by modern computers despite considering advancements in processor speeds based on Moore's law.