Montgomery modular‐multiplication method and systolic arrays suitable for modular exponentiation

Abstract

AbstractThe Montgomery method is known as a method to execute modular multiplications without using divisions, and several systolic arrays have been proposed for execution of the Montgomery method. A problem in the Montgomery method is that the number of output bits may exceed the number of input bits. In the past implementations, the size of the output must be examined and corrected each time the method is executed, which is an obstacle in improving the efficiency.From such a viewpoint, this paper derives the general condition so that the size of the output need not be examined each time the Montgomery method is executed and proposes two types of systolic arrays that execute the Montgomery method under that condition. These arrays are more efficient than the systolic array proposed previously by the authors for modular multiplications. The method is effective and practical for VLSI implementation such as on a chip.