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How to combine the keys in the Triple Diffie-Hellman (3DH) key exchange?

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I was reading up on the Triple Diffie-Hellman (3-DH) key exchange and noticed that the wikipedia description [1] is different from the the original protocol definition [2] and the modified definition [3] they reference.

Two users have two key pairs each; $a, A$ and $x, X$ for one user and $b, B$ and $y, Y$ for the other. $H$ is a key derivation function. Is there any difference between the following two shared secrets that can be derived?

  • $K = H(Ay, Xb) = H(Ya, Bx)$
  • $K = H(Yx, Bx, Ya) = H(Xy, Xb, Ay)$

The difference being the addition of the $Yx = Xy$ values to the key derivation.


References:

  1. Wikipedia
  2. Original definition page 15
  3. Modified definition page 560-561
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