Here’s a scenario. Let’s pretend NSA has intercepted a message encrypted with a 128 bit key and they really want to crack it. Keep in mind: your phone easily encrypts messages with 128 bit keys in a couple milliseconds. This sort of crypto is nothing special, and your computers do crypto operations like this each time you use a web browser.
To do this, NSA needs to build a cluster of parallel processors trying to decrypt the message with different keys until they get it right. They’ll guess that the key is 0, then 1, then 2, then 3, then 4, then 5, and so on. By the time they get to 2^128, they will have completed an exhaustive search of the keyspace and definitely will have cracked it.
Now let’s pretend the NSA has a budget of $100 trillion (in reality, they don’t have nearly that much money). Let’s also say that they can buy $50 computers that can test 100,000 keys a second (try making your Raspberry Pi do that, I dare you). Spending the entire $100 trillion at $50 a pop, they can afford two trillion computers. At 100,000 guesses per second, the entire cluster of two trillion computers can make 200,000,000,000,000,000 guesses per second.
So how many seconds will it take to guess all 2^128 possible keys?
1,701,411,834,604,692,317,316 seconds.
Which is 28,356,863,910,078,205,288 minutes.
Which is 472,614,398,501,303,421 hours.
Which is 19,692,266,604,220,975 days.
Which is 53,951,415,354,030 years.
Which is 53,951,415,354 millennia.
Since the key could be any number between 0 and 2^128, chances are the key will be found in half that time. So 27 billion millennia then?
That’s a long time to wait to crack the crypto on a single message. And I greatly exaggerated the resources of the NSA. In reality, they’d be waiting a lot longer. Another way to put it is this: If all the combined computing power currently available to the human race were devoted to decrypting this one single message, the sun would die out before it was cracked.
https://micahflee.com/2013/01/no-really-the-nsa-cant-break-your-crypto/https://i.imgur.com/ag3KQ0L.pngHere is an analogy I like.
The odds of winning the jackpot on the powerball lotto is 1 in 175,223,510.
Compare that to the odds of 2 people generating the same seed, 1 in 280,000,000,000,000,000,000,000,000,000,000,000,000, and the idea begins to come into focus.
You are more likely to win the jackpot on the powerball 4 times in a row than you are of generating the same seed.
To simply create and store every possible combination of Seeds, you'd need to fill our solar system with 1TB harddrives.
