Strictly speaking, isn't "guess my large number" sufficient to break most encryption protocols that don't rely on security by obscurity? It's just that the numbers are normally larger by dozens of orders of magnitude.
Yes, but you are ignoring the time factor. Assume I'm going to die of natural causes in 60 years. If it takes a minute to guess a 6 digit number, that is really bad. If it takes 1000 years to guess a number that is larger by dozens of orders of magnitude, odds are pretty good I'm going to die of natural causes before the attacker guesses the right number.
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Strictly speaking, isn't "guess my large number" sufficient to break most encryption protocols that don't rely on security by obscurity? It's just that the numbers are normally larger by dozens of orders of magnitude.
Yes, but you are ignoring the time factor. Assume I'm going to die of natural causes in 60 years. If it takes a minute to guess a 6 digit number, that is really bad. If it takes 1000 years to guess a number that is larger by dozens of orders of magnitude, odds are pretty good I'm going to die of natural causes before the attacker guesses the right number.