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Tate Pairing in Cryptography: Tripartite<br />
Diffie-Hellman Key Exchange<br />
Public Knowledge: A group E(F p ) and a point P of order n.<br />
ALICE BOB CHANTAL<br />
Secret 0 < a < n 0 < b < n 0 < c < n<br />
Compute Q Alice = aP Q Bob = bP Q Chantal = cP<br />
Reveal Q Alice Q Bob Q Chantal<br />
Compute τ n (Q Bob, Q Chantal ) a τ n (Q Alice ,Q Chantal ) b τ n (Q Alice ,Q Bob ) c<br />
These three values are equal to τ n (P,P) abc<br />
Security (presumably?) relies on Discrete Log Problem in F p *
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