> My understanding is that to convert the form of ecc key from compressed to
> uncompressed and from uncompressed to compressed require the knowledge of
> the ECC private key.
> Is my understanding correct?

You might want to have a look at sections 2.3.3 and 2.3.4 in

http://www.secg.org/download/aid-780/sec1-v2.pdf

No knowledge of the private key is needed.

Regards,
Martin
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