The key point in this paper is the definition of new mathematical concepts based on point doubling and addition on the Edward curve group and matrix power functions. The basic idea is known as the Edward scalar multiplication matrix function (E_dSMMF). Also proposed is a modification to the Diffie-Hellman and ElGamal schemes in the Edward curve cryptosystem, which is more secure than the original because the discrete logarithm problem is computationally infeasible to solve.