The elliptical curve system has received great interest in the science of security systems, and this has a great number of advantages. When linked with chaotic systems, it gave a broad comprehensiveness in the science of finding common keys between the two parties or in a system as a server that distributes the common keys among the participants in the distress. The proposed algorithm reduces processor load, reduces power consumption, increases processing speed, enhances storage efficiency , requires smaller certificates, and is good at saving bandwidth. Where ECC gives high-level arithmetic operations ECC is an algebraic structure in wide areas for a large number of points and any point in the Cartesian coordinates, as well as for a number of prime numbers generated from the chaotic three-dimensional system using the multiplication and addition algorithm of the elliptical curved system. This paper suggested a new event in the implementation method: the inputs to the elements of the controlling parameters and the initial conditions of the symmetric chaotic functions produce an ECC by a secret shared key between two parties or a number of parties participating in the group, and all these points of the share keys lie on the points of the curve. and this key technology is available for authentication, confidentiality, and non-repudiation.