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To: precisionshootist

Encryption was my job.
For Uncle Sam.


101 posted on 01/13/2020 10:41:34 PM PST by Mariner (War Criminal #18)
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To: Mariner
Heres what one other expert on 256bit AES cracking:

Time and energy required to brute-force a AES-256 encryption key.

I did a report on encryption a while ago, and I thought I'd post a bit of it here as it's quite mind-boggling.

AES-256 is the standardized encryption specification. It's used worldwide by everyone from corporations to the US government. It's largest key size is 256 bits. This means that the key, the thing that turns encrypted data into unencrypted data, is string of 256 1s or 0s.

With each character having two possibilities (1 or 0), there are 2256 possible combinations. Typically, only 50% of these need to be exhausted to yield the correct key, so only 2255 need to be guessed. How long would it take to flip through each of the possible keys?

When doing mundane, repetitive calculations (such as brute-forcing or bitcoin mining), the GPU is better suited than the CPU. A high-end GPU can typically do about 2 billion calculations per second (2 gigaflops). So, we'll use GPUs.

Say you had a billion of these, all hooked together in a massively parallel computer system. Together, they could perform at 218 flops, or

2,000,000,000,000,000,000 keys per second (2 quintillion)

1 billion gpus @ 2 gigaflops each (2 billion flops)

Since there are 31,556,952 seconds in a year, we can multiply by that to get the keys per year.

*31,556,952

=6.311390425 keys per year (~10 septillion, 10 yottaflops)

Now we divide 2255 combinations by 6.311390425 keys per year:

2255 / 6.311390425

=9.173263150 years

The universe itself only existed for 14 billion (1.410) years. It would take ~6.740 times longer than the age of the universe to exhaust just half of the keyspace of a AES-256 keys.

On top of this, there is an energy limitation. The Landauer limit is a theoretical limit of energy consumption of a computation. It holds that on a system that is logically irreversible (bits do not reset themselves back to 0 from 1), a change in the value of a bit requires an entropy increase according to kTln2, where k is the Boltzmann constant, T is the temperature of the circuit in kelvins and ln2 is the natural log(2).

Lets try our experiment while considering power.

Most high-end GPUs take around 150 watts of energy to power themselves at full load. This doesn't include cooling systems.

One billion GPUS will require: 1 billion gpus @ 150 watts
150,000,000,000 watts (150 gigawatts)
1.511 watts

This is enough power to power 50 million american households.

The largest nuclear power reactors (Kashiwazaki-Kariwa) generate about 1 gigawatt of energy.

1.511 watts / 1 gigawatt = 150

Therefore, 1 billion GPUs would require 150 nuclear power plant reactors to constantly power them, and it would still take longer than the age of the universe to exhaust half of aN AES-256 keyspace.

1 billion GPUs is kind of unrealistic. How about a supercomputer?

The Tianhe-2 Supercomputer is the world's fastest supercomputer located at Sun Yat-sen University, Guangzhou, China. It clocks in at around 34 petaflops.

Tianhe-2 Supercomputer @ 33.86 petaflops (quadrillion flops) =33,860,000,000,000,000 keys per second (33.86 quadrilion)

3.38616 * 31,556,952 seconds in a year
2255 possible keys 2255 / 1.068518424

=1.068518424 keys per year (~1 septillion, 1 yottaflop)

=5.418347952 years

That's just for 1 machine. Reducing the time by just one power would require 10 more basketball court-sized supercomputers. To reduce the time by x power, we would require 10x basketball court-sized supercomputers. It would take 1,038 Tianhe-2 Supercomputers running for the entirety of the existence of everything to exhaust half of the keyspace of a AES-256 key.

And, Mariner, these calculations are assuming that the key would be hit in the first half of the key set. The odds of that are only 50%.

Another encryption specialist did a calculation on the energy to do the entire key set. . . It exceeded the energy available in the universe. ROTFLMAO! His conclusion was that any computer that could do the job would need to be made out of something other than matter, run on something other than energy, and extend into another universe.

121 posted on 01/14/2020 2:18:06 AM PST by Swordmaker (My pistol self-identifies as an iPad, so you must accept it in gun-free zones, you hoplophobe bigot!)
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To: Mariner
Encryption was my job.
For Uncle Sam.

When. Since you linked to a computer from 1966, I suspect that might be when you were doing it.

156 posted on 01/14/2020 11:08:56 AM PST by Swordmaker (My pistol self-identifies as an iPad, so you must accept it in gun-free zones, you hoplophobe bigot!)
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