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In this paper, we do a cryptanalyse of the so called ``Strong Diffie-Hellman-DSA Key Exchange (briefly: SDH-DSA-KE)" and after we propose ``Strong Diffie-Hellman-Exponential-Schnnor Key Exchange (briefly: SDH-XS-KE)" which is an improvement for efficiency and security. SDH-XS-KE protocol is secure against Session State Reveal (SSR) attacks, Key independency attacks, Unknown-key share (UKS) attacks and Key-Compromise Impersonation (KCI) attacks. Furthermore, SDH-XS-KE has Perfect Forward Secrecy (PFS) property and a key confirmation step. The new proposition is not vulnerable to Disclosure to ephemeral or long-term Diffie-Hellman exponents. We design our protocol in finite groups therefore this protocol can be implemented in elliptic curves.

In our paper paper we propose a new binary elliptic curve of the form $a[x^2+y^2+xy+1]+(a+b)[x^2y+y^2x]=0$. If $m\geq 5$ we prove that each ordinary elliptic curve $y^{2}+xy=x^{3}+\alpha x^2+\beta, \beta\neq 0$ over $\mathbb{F}_{2^m}$, is birationally equivalent over $\mathbb{F}_{2^m}$ to our curve. This paper also presents the formulas for the group law.