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Better key negotiations

There exists a secure protocol(Diffie-Hellman) with 2 modular exponentiation operations for negotiating a key with no authentication. There exists a secure protocol(SPEKE, SRP, EKE..) with 2 exponentiations for negotiating a key with mutual authentication. Doesn't this suggest the existence of a 2 exponentiation protocol for authenticating only one side? Does one exist? It would be an improvement over what's now used with three exponentiations by the server.

Watson Ladd
"Those who would give up Essential Liberty to purchase a little Temporary Safety deserve neither Liberty nor Safety."
-- Benjamin Franklin

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