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The purpose of this paper is to study sender authenticated key agreements by a third party, which uses the received parameters to verify the fact that a sender of a message knows his long-term private key. In particular, we propose a standard model for the protocol among three entities for the first time. The security of this protocol depends on the difficulty to solve two new problems related to one-way isomorphisms and the co-bilinear Diffie-Hellman problem on multiplicative cyclic groups. It is the first time that the security of a key agreement has been formally proved by using negligible probability. We believe that our contribution gives many applications in the cryptographic community.