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 of solving two new problems related to one-way isomorphisms and the decision co-bilinear Diffie-Hellman problem on multiplicative cyclic groups. It is the first time that the security of a key agreement has been formally proven by using negligible probability. We believe that our contribution gives many applications in the cryptographic community.

In this paper, we examine the computational Diffie-Hellman problem and decisional Diffie-Hellman problem in 3-rd order linear feedback shift register and show that the shift register based Diffie-Hellman problems are equivalent to the Diffie-Hellman problems over prime subgroup of GF(p3e) respectively. This result will be useful in constructing new cryptographic primitives based on the hardness of the shift register based Diffie-Hellman problems.