Thread: Prime numbers
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Old 2008-11-08, 10:11   #7
NBtarheel_33
 
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"Nathan"
Jul 2008
Maryland, USA

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Quote:
Originally Posted by Unregistered View Post
Is it possible to get all known prime numbers? (We want to brute force 1024 bits RSA key)
Think about it - obviously, the key is designed to be used for secure encryption, hence the designers and users want something that is going to be nigh impossible to break. If what you are thinking of doing were possible, believe me, RSA would be using much, much, much larger keys that would ensure that your brute force attack would take a very, very, very, long time. This is, in fact, why RSA has increased its key size over the years, as advances in computing power have made such brute-force attacks feasible for smaller keylengths.

The only thing that saves our butts with regard to encryption (at least as it stands today) is the fact that integer factorization is essentially impossible for arbitrary integers of any decent size, unless they are of a special form (e.g. Mersenne numbers). Integer factorization problems very, very quickly run into the realm of "oops, the universe is not big enough to hold this calculation".
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