High radix implementation of Montgomery multipliers with CSA

Abstract

Modular multiplication is the key operation in systems based on public key encryption, both for RSA and elliptic curve (ECC) systems. High performance hardware implementations of RSA and ECC systems use the Montgomery algorithm for modular multiplication, since it allows results to be obtained without performing the division operation. The aim of this article is to explore various modified structures of the Montgomery algorithm for high speed implementation. We present the implementation of a modified Montgomery algorithm with CSA and with different radix. In order to optimize the implementation regarding operation speed, we considered carry save adders structures and the Booth recoding scheme. The structure used in this paper simplifies the computation of the partial products avoiding the use of memories to store pre-calculated data for partial products which cannot be achieved by the shifting operation. The result shows that high-radix implementations are better for high speed applications.