Low power modular integer exponentiation using discrete logarithm transformation

Abstract

Exponentiation is an important mathematical operation in many areas, and is constantly being researched for more efficient methods. This paper presents a power efficient implementation of integer modular exponentiation using discrete logarithm transformation. By transforming the base of an exponent, this method is able to perform modular exponentiation without the use of multipliers. Originally developed and implemented for high speed applications, this method has been modified and implemented for low power while maintaining comparable performance. The design is created and simulated with a repeative-square design for comparison purpose. The two circuits are compared in terms of speed and power consumption. Results show that for bus sizes greater than 32 bit, the proposed design is able to use only approximately 40% of the power that the repeative-square counterpart consumes.