The present invention is a polynomial-based hash function involving an ERINDALE-PLUS hashing algorithm. The function may involve several elements, including splitting with jumping, masking and bit string generation which generally involves representing an initial sequence of bits as a specially constructed set of polynomials. The means of achieving the function may involve methods that achieve improved speeds, such as requirements related to the size of the bit strings to cause the bit strings to be compatible with splitting and jumping and to involve iterated masking of a degree greater than 0. Additionally the function may involve recursive padding methods and a construction of MAC for considered hash function. The sum of the elements of the present invention is the provision of enhanced security as well as improved speed of processing for messages. Thus, messages processed by way of the present invention may be less prone to attack.