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I understand how ECC works for the point multiplications and stuff.
All we normally do is to multiply a scalar number (lets say d as a private key) with the base point generator G to get a public key point on an elliptic curve.
I am trying to tweak the algorithm for some other purposes so I am just wondering whether an operation like G*G which is a point multiply another point is possible or not. And if it is possible how can we calculate that?

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Such an operation is possible.
The ways of calculating that appear to be different for each curve.

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  • $\begingroup$ Sounds nice. What about its security? Is this operation reversible by dividing the result to a G? $\endgroup$ – abeikverdi Apr 22 '15 at 6:31
  • $\begingroup$ That is the Fixed Pairing Inversion problem. $\;$ $\endgroup$ – user991 Apr 22 '15 at 6:43
  • $\begingroup$ Thanks a lot. I don't have enough points to vote your answer up but it really helped. $\endgroup$ – abeikverdi Apr 22 '15 at 7:15

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