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Is it possible to extract/generate private key from captured SSL traffic?

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I'm quite new so there's a deal and If anyone could help me with this i would be so grateful, 'cause I have been looking for answer since Thursday and didn't find anything : I have captured SSL traffic with several valid handshakes, containing, Server Hello, Client Hello, Certificates, Key Exchange etc. and what I tried to do was extract the SSL cert and check if I can made a valid SSL connection, ok I figured out that apparently I can't without Private Key, right? And this is my question, is it anyway to get this key from my captured traffic?


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