Wouldn't it be possible to create as many as possible key pairs for the RSA encryption and then determine from a public key which the corresponding private key is ?

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    Short answer: No, there are too many possible key pairs.
    – SEJPM
    Mar 22, 2016 at 18:21

1 Answer 1


The answer to your question is very closely related to this post: https://math.stackexchange.com/questions/263588/how-many-all-prime-numbers-p-with-length-of-bits-of-p-1024-bits

Via. the prime number theorem we can calculate that there are approximately 1.26 * 10305 prime numbers less than 21024. That is a lot of numbers. For scale, a terabyte is 1012 bytes!

So yes, though this brute force approach is theoretically doable we don't, and won't, have the resources for a very long time!

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    replace "for a very long time" with "it's physically impossible!" as per this answer
    – SEJPM
    Mar 22, 2016 at 19:23
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    @SEJPM Currently believed to be physically impossible would be more accurate. Once upon a time, heavier than air flying machines were physically impossible.
    – Phil Lello
    Mar 22, 2016 at 20:43

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