System and method for the calculation of a polynomial-based hash function and the erindale-plus hashing algorithm

10) A method of application of a polynomial-based hash function to a message sent by a user from a computer, characterized in that it comprises the following steps:

• a) calculating a hash output utilizing the polynomial-based hash function by one or more of the following steps:
• i) applying a splitting with jumping function to the message to generate splitting with jumping outputs;
• ii) applying a masking function to the splitting with jumping outputs to generate masking outputs;
• iii) applying a bit string generation function to the masking outputs to generate bit strings outputs;
• and
• iv) applying a padding function to the bit strings outputs to generate padding outputs;
• b) processing the padding outputs by one or more processing functions operable to generate a set of polynomials;
• c) performing the incorporation of the set of polynomials with the message to generate an output that averts attacks upon the security of the message.

20) A computer system characterized in that it comprises software to program existing computer hardware to:

• a) receive a message sent by a sender;
• b) apply one or more polynomial-based hashing functions to the message to produce a hash output, utilizing one or more of the following elements:
• i) a splitting with jumping function;
• ii) a masking function;
• iii) a bit string generation function;
• and
• iv) a padding function;
• c) process the hash output by one or more processing functions operable to generate an output that averts attacks upon the security of the message.

21) A polynomial-based hash function operable by way of a computer program including computer instructions operable to averting attacks upon a message sent by a sender characterized in that it comprises:

• a) one or more of the following elements to produce a hash output, each facilitating a parameterized inner structure:
• i) a splitting with jumping function;
• ii) a masking function;
• iii) a bit string generation function;
• and
• iv) a padding function;
• b) one or more processing functions operable to generate an output that averts attacks upon the security of the message.