A Division-Free Toom–Cook Multiplication-Based Montgomery Modular Multiplication

Abstract

Toom-Cook multiplication is a theoretically more efficient multiplication algorithm than traditionally used Karatsuba and schoolbook multiplication but is rarely used in practical hardware designs due to its inherent exact divisions, which are time-consuming and difficult for parallel and serial acceleration. This brief proposes a method of division-free Toom-Cook multiplication based Montgomery modular multiplication, which makes it possible for Toom-Cook multiplication to be applied in practical and efficient hardware implementations. We also provide a hardware implementation of modular multipliers of 256 bits and 1024 bits with advantages on area-time-product over previous researches.