Algorithm for unified modular division in GF(p) and GF(2n) suitable for cryptographic hardware

A unified algorithm to compute modular division in both GF(p) and GF(2ⁿ) fields is presented. It uses a counter variable to keep track of the difference between two field elements, and in this way eliminates the need for comparisons which are usually expensive and time-consuming. The computations in both fields are performed using additions/subtractions and bit shifts, besides using a simple control flow, which makes it suitable for hardware implementation.