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al-right, I need some examples of hard and long RSA keys cause i think i have found vulnerability in RSA. i need you to give me few hard Values of n (which is pxq) and i will tell you what p and q are(don't tell me p and q, just tell me n) PLEASE I NEED TO SEE IT!

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    $\begingroup$ I think this question uniquely qualifies for the "too broad" close reason: there are (literally) an infinite number of possible answers. $\endgroup$ – Reid May 20 '15 at 3:26
  • $\begingroup$ @Reid : $\:$ :-D $\;\;\;\;$ $\endgroup$ – user991 May 20 '15 at 3:36
  • $\begingroup$ Sorry, but unless you have discovered a new branch of mathematics, it is overwhelmingly likely that you have not found a way to quickly factor large primes. $\endgroup$ – Stephen Touset May 20 '15 at 4:20
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    $\begingroup$ I have found a vulnerability in RSA, too. For example, I can factor $21 = 3\times 7$. I just have to deal with the last thingie: how to apply it to very, very big numbers. That's it. $\endgroup$ – fkraiem May 20 '15 at 8:43
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    $\begingroup$ You can retrieve certificates from google with the openssl (and sed) commands: "openssl s_client -connect www.google.com:https < /dev/null | sed -ne '\/-----BEGIN CERTIFICATE-----/,\/-----END CERTIFICATE-----/p' | openssl x509 -noout -modulus" $\endgroup$ – Steve Peltz May 21 '15 at 5:05
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Here's a 2048-bit modulus $n$:

23345135319098428695918096856351736691605733130699443284127783899530798300904263761969678228722978488932525152955208774038661063724795894350101766091648183643636110431139209906713716077186478554224587745514191720761948637234911856612912494476420747968037052472880258891484744014484452559576872262526136662041614283437793117377679057048155066144396797991089164008590146279602387924918463421293422838064353499217789275561842179096901894289131036262707390743621266197100148615760893198749965409128055493921274609123555724795514808799093273087781413458495123664728027138459685630533762158565719480811485043587128111559163

in decimal. I don't mean to be negative, but if you cannot manage to find a 2048-bit RSA modulus by yourself, it's probably unlikely that you've found a vulnerability.

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  • $\begingroup$ is this the value of n(which is pxq)? just need to make sure $\endgroup$ – AKC May 20 '15 at 1:31
  • $\begingroup$ @user3651521: Yes. That is $n=pq$ where $p,q$ are distinct primes roughly 1024 bits in size. $\endgroup$ – Reid May 20 '15 at 1:31
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    $\begingroup$ Factoring RSA-2048 would earn more brownie points, although the $200,000 prize is no longer on offer, unfortunately. $\endgroup$ – r3mainer May 20 '15 at 13:12
  • $\begingroup$ Had I been at my computer before the question was closed, I'd have posted RSA-2048. If you factor that, it shows people that you hadn't just created your own key and "factored" it, so is more helpful in showing off. $\endgroup$ – cpast May 20 '15 at 14:10
  • $\begingroup$ Ah, yeah, RSA-2048 would have been a better choice in retrospect. Truth be told, I just completely forgot about it. $\endgroup$ – Reid May 20 '15 at 14:16

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