The message authentication code with elliptic polynomial hopping provides methods for the generation of message authentication codes (MACs) utilizing elliptic curves, which are based on the elliptic curve discrete logarithm problem. The elliptic curve discrete logarithm problem is well known to be a computationally “difficult” or “hard” problem, thus providing enhanced security for the MACs. Different elliptic polynomials are used for different blocks of the same plaintext, each elliptic polynomial for each message block being selected at random using an initial secret key and a random number generator.