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Having some specific ECDSA curve and a private key, how does one calculate the public key? I am having a hard time finding the algorithm and equations for it.

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up vote 5 down vote accepted

The write up on Wikipedia is pretty good. I won't go into all the detail that they do there, but your private key is a randomly selected integer $d_A$ selected from $[1,n-1]$ where $n$ is the order of the group. The public key is $Q_A=d_AG$ where $G$ is the base point on the curve defined in the publicly agreed upon parameters.

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