# Deriving 2 shared secrets from one private key and 2 different public keys

I have a key pair, say $(d, Q)$. I send my public key $Q$ to 2 different people. I also get their public keys $Q_1$ and $Q_2$. Now I can derive 2 shared secrets, $d*Q_1$ and $d*Q_2$. The 2 other people can also derive secrets $d_1*Q$ and $d_2*Q$. Assuming all key pairs were generated from the same elliptic curve, is it safe to use both the shared secrets in the same session for 2-way communication?

• what does it mean by "derive 2 shared secrets , $d*Q_1$ ..." ? . Also looks like some text book problem ? Jun 12 '15 at 3:09
• It's very much a real world problem. What I mean by 2 shared secrets is using the same private key, pairing it with 2 different public keys (all from the same curve) to generate 2 shared secrets using Diffie-Hellman. (The shared secrets will be $d*Q_1$ and $d*Q_2$ on one side and $d_1*Q$ and $d_2*Q$ on the other side.) Keep in mind that both shared secrets are being used at the same time(To generate symmetric keys for example).
– user25016
Jun 12 '15 at 9:45