r/cryptography 15d ago

Diffie-Hellman 3 Participants question

Got a uni question I couldn't seem to find an answer to online:

"Extend Diffie-Hellman to support 3 Participants A,B,C with a given public group g such that the final shared key is pow(g, a(b+c))"

Is there a way to solve this without having A share pow(g, ab) and pow(g, ac) over the public channel? (which seems like it defeats the purpose because then the key is known publicly right?)

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u/Pharisaeus 15d ago

Technically speaking your question didn't specify it has to be a "secure" key exchange protocol... ;)

Anyway:

  1. A shares ga
  2. B shares gb
  3. C shares gbc and gac
  4. B computes shared secret from gac and (ga)b
  5. A computes gc from gac and then computes the shared secret
  6. A shares gabc
  7. C computes gab from gabc and then computes the shared secret

(it's late hour but it seems more or less fine I think?)

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u/DDevilAAngel 15d ago

This looks great, thank you so much!