Cryptographic hash generation system

A device effective to generate a hash of a string, the device comprising:

• a memory, wherein the memory is effective to include
• a first function,
• a first list of first monoid elements, and
• an initial monoid element;
• a first module effective to receive the string and divide the string into a sequence of blocks;
• a second module in communication with the first module and the memory, the second module effective to associate blocks in the sequence of blocks with respective monoid elements in the first list of first monoid elements to produce a second list of second monoid elements;
• a third module in communication with the second module and with the memory, the third module effective to
• receive a first one of the second monoid elements,
• receive the initial monoid element,
• receive the first function,
• apply the first function to the initial monoid element and the first one of the second monoid elements to produce a first calculated monoid element, and
• evaluate an action of the initial monoid element on the first function to produce a second function;
• a fourth module in communication with the second module and the third module, the fourth module effective to
• receive a second one of the second monoid elements,
• receive the first calculated monoid element,
• receive the second function, and
• apply the second function to the first calculated monoid element and to the second one of the second monoid elements to produce a second calculated monoid element.