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In a certificate-less cryptography, I have learned that – to resolve the key escrow problem of IBE – the concept of a partial private key is used.

Now, consider the following Scenario:

  • After verifying User's Identity, KGC generates a partial-private key for the respected user.
  • After accepting the partial-private keys from the Key Generation Center (KGC), User generates a pair of public & private keys.

Question: How does the Key Generation Center know that the generated pair public & private key is computed using the sent partial-private key of the respected user?

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Are you asking about some specific proposed CT-less scheme? $\:$ Even schemes in which the Key Generation Center can know that don't necessarily let it achieve such knowledge in the same way. $\hspace{.55 in}$ –  Ricky Demer Apr 9 '14 at 15:37

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