What takes 1.8 million billion billion billion billion billion billion years to find?

Question

4-bit key
4-bit key

So what takes 1.8 million billion billion billion billion billion billion years, on average, to find, and is only 256 things long? Well it is the time it would take you, or to be more precise, your high-powered computer, to find the key used in a 256-bit encryption process. This calculation takes into account that you would be using one of the best computers around, which would be able to process at 1,000,000,000 keys per second, which is much faster most normal desktop computer. The following tables shows you how long it would take for different key sizes:

http://www.asecuritysite.com/encryption/keys

So you can’t understand why it would take so long? Well the number of keys that we have relates to the number of bits that we have in the key. So a 4-bit key would have 8 different keys from 0000 to 1111. An 8-bit key has 256 keys, a 20-bit key has over 1 million keys, and so on. Mostly we start with something like a 56-bit key, which gives us:

72,057,594,037,927,936

different keys. So if we use a computer which checks 1 billion keys per second, then the time to check one key will be 1ns, so the time to find, on average, the key will be:

T = 72,057,594,037,927,936 * 1×10^-9 / 2

which is 36,028,797 seconds, or 600,479 minutes, or 10,007 hours or 416 days, or 1.14 years. But why do we go from just over a year to billions of years? Well for ever bit that we add, we double the key space. So 57 bits takes 2.28 years, 58 bits takes 4.56 years, and so on. Thus it doesn’t take too long to get to a point where it takes billions of years. So for 256-bits, we get:

115,792,089,237,316,195,423,570,985,008,687,907,853,269,984,665,640,564,039,457,584,007,913,129,639,936

different keys, so if you do the calculation you get:

1,835,871,531,540,400,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 years

which is a LONG TIME!

Conclusion

For a completely random key, 256-bits is completely uncrackable with today’s, tomorrow’s computers. If we were to do it, we would need a quantum computer, which could parallelise the computation, and perform them at the speed of light. But the thing we must ask is … are the keys actually random? If not, then it’s a whole different calculation?

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