1. A computer-implemented method of determining a modular remainder with respect to a polynomial of a message comprised of a series of segments, comprising: accessing a strict subset of the segments representing the message, the strict subset consisting of the most significant segments representing the message; transforming the strict subset of segments into a smaller set of segments; redefining the segments representing the message as a sequence consisting of the smaller set of segments and segments excluded from the strict subset of segments; repeating the accessing, transforming, and redefining at least once to generate an output set of segments representing the message; determining the modular remainder based on the output set of segments; and storing the determined modular remainder.