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I admit I don't know a lot about the math behind Curve25519 and the DH exchange based on it.

I'm asking if after publishing the result of this operation:

ephemeral_share = X25519(ephemeral_secret, BASEPOINT)

Can ephemeral_secret be found by whomever obtains ephemeral_share, given that they know the used curve (and therefore the curve's base point)?

It's not that I don't trust Filippo's judgment (the above is taken from a 2019 entry on his blog); I'm just trying to make sure I understand things correctly.

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Can the ephemeral_secret be found by whomever obtains the ephemeral_share, given that they know the curve that was used (and therefore the curve's basepoint)?

If the design goals of the X25519 implementation at hand are met, and ephemeral_secret was generated randomly and kept secret, no. That would be breaking the Discrete Logarithm Problem as it stands for X25519.

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