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1

ECDH is included in the ciphersuites, so the only answer is: yes, this should be possible. For your further research, it might help to know that Crypto.SE features a lot of Q&As related to “OpenSSL ECDH”. Also see the related documentation at the OpenSSL wiki for practical code examples showing how to use ECDH in OpenSSL, how to use the low-level APIs ...


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For completeness, here is how to compute $d$ without resorting to the value of public exponent $e$. Compute $\delta = \gcd(p-1,q-1)$; Define $p' = p-1$ and $q' = (q-1)/\delta$; Compute $i_{q'} = (q')^{-1} \bmod p'$ and $d_{q'} = d_q \bmod q'$; Return $d = d_{q'} + q'[i_{q'} (d_{p}-d_{q'}) \bmod p']$. Note that the so-obtained value for $d$ is defined ...



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