CDMI: A Clockwise-Displacement Algorithm to Compute Multiplicative Inverse

A multiplicative inverse (MI) algorithm is used in several fields, like cryptography algorithms. There are many MIs, however, these algorithms suffer from using several multiplication and division operations, which take more execution time than additions and subtractions. We created a new algorithm called Clockwise-Displacement (CDMI) by using addition and subtraction operations in the iterative steps instead of multiplications and divisions. Additionally, numerous MIs face the undecidable problem because of the floating-point issue. Whereas, CDMI tackles this issue by converting the domain from the floatingpoint space to integer space. Therefore, CDMI declines the time consuming to calculate the multiplicative inverse by applying fewer divisions and multiplications (expensive operations) and addresses the rounding error issue in some MI Algorithms.