Efficient architectures for implementing montgomery modular multiplication and RSA modular exponentiation on reconfigurable logic

Abstract

This paper presents a review of some existing architectures for the implementation of Montgomery modular multiplication and exponentiation on FPGA (Field Programmable Gate Array). Some new architectures are presented, including a pipelined architecture exploiting the maximum carry chain length of the FPGA which is used to implement the modular exponentiation operation required for RSA encryption and decryption. Speed and area comparisons are performed on the optimised designs. The issues of targeting a design specifically for a reconfigurable device are considered, taking into account the underlying architecture imposed by the target technology.