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    $\begingroup$ Does Proxy Re-Encryption solve your problem? $\endgroup$ Commented Dec 7, 2015 at 19:18
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    $\begingroup$ According to the relations you have written out, someone with $Encrypted1$ could pick a random $Key2$, SomeAdditionalCryptoFunction it, SomeDecryptFunction it, and arrive at the original $Data$. Is this really what you mean? $\endgroup$ Commented Dec 7, 2015 at 19:20
  • $\begingroup$ If the user is capable of generating a new key, and performing some transform on it such that the new key can decrypt the original data, it follows that the user can decrypt the original data. So why not simply decrypt it and reencrypt it with the second key? $\endgroup$ Commented Dec 7, 2015 at 19:27
  • $\begingroup$ poncho, Stephen, I added an edit to clarify, I hope it does. @SEJPM This looks hopefull! I will check it out! $\endgroup$ Commented Dec 7, 2015 at 20:27
  • $\begingroup$ So you want traitor tracing when a key gets leaked? In that case you might be interested in broadcast encryption. Or why is using the same key problematic? $\endgroup$ Commented Dec 7, 2015 at 20:37