Comparison of three modular reduction functions

Three modular reduction algorithms for large integers are compared with respect to their performance in portable software: the classical algorithm, Barrett’s algorithm and Montgomery’s algorithm. These algorithms are a time critical step in the implementation of the modular exponentiation operation. For each of these algorithms their application in the modular exponentiation operation is considered. Modular exponentiation constitutes the basis of many well known and widely used public key cryptosystems. A fast and portable modular exponentiation will considerably enhance the speed and applicability of these systems.